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i-manager's Journal on Mathematics (JMAT)

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Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method

Most Cited

Volume 7 Issue 3 July - September 2018

Research Paper

On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces

Muhammed Recai Turkmen *

Assistant Professor, Department of Mathematics and Science Education, The Afyon Kocatepe University, Turkey.

Türkmen, M. R. (2018). On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces, i-manager's Journal on Mathematics, 7(3), 1-9. https://doi.org/10.26634/jmat.7.3.14868

Abstract

In this paper, the author has introduced the concept of lacunary summable and lacunary statistical convergence in fuzzy n-normed spaces. At the same time, the author has introduced condition of being lacunary statistically Cauchy sequence with respect to a fuzzy n-norm. The author has also studied the relation between these concepts and gave some properties of lacunary statistical convergence sequences in fuzzy n-normed spaces.

References

[1]. Altınok, H., Altın, Y., & Et, M. (2004). Lacunary almost statistical convergence of fuzzy numbers. Thai Journal of Mathematics, 2(2), 265-274.

[2]. Bag, T., & Samanta, S. K. (2008). Fixed point theorems in Felbin's type fuzzy normed linear spaces. Journal of Fuzzy Mathematics, 16(1), 243.

[3]. Diamond, P., & Kloeden, P. E. (1994). Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific.

[4]. Dündar, E., Ulusu. U., & Pancaroğlu, N. (2016). Strongly J₂ -Lacunary Convergence and J₂ -Lacunary Cauchy Double Sequences of Sets. The Aligarh Bulletin of Mathematics, 35 (1-2), 1-15.

[5]. Fast, H. (1951). Sur la convergence statistique. In Colloquium Mathematicae, 2(3-4), 241-244.

[6]. Felbin, C. (1992). Finite dimensional fuzzy normed linear space. Fuzzy Sets and Systems, 48(2), 239-248.

[7]. Fridy, J. A. (1985). On statistical convergence. Analysis, 5(4), 301-314.

[8]. Fridy, J. A., & Orhan, C. (1993). Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43-51.

[9]. Matloka, M. (1986). Sequences of fuzzy numbers. Busefal, 28(1), 28-37.

[10]. Misiak, A. (1989). n-inner product spaces. Mathematische Nachrichten, 140(1), 299-319.

[11]. Mizumoto M., & Tanaka, K. (1979). Some properties of fuzzy numbers, North-Holland (Amsterdam): Advances in Fuzzy Set Theory and Applications.

[12]. Nanda, S. (1989). On sequences of fuzzy numbers. Fuzzy Sets and Systems, 33(1), 123-126.

[13]. Narayanan, A., & Vijayabalaji, S. (2005). Fuzzy n-normed linear space. International Journal of Mathematics and Mathematical Sciences, 2005(24), 3963-3977.

[14]. Nuray, F. (1998). Lacunary statistical convergence of sequences of fuzzy numbers. Fuzzy Sets and Systems, 99(3), 353- 355.

[15]. Nuray, F., & Savaş, E. (1995). Statistical convergence of sequences of fuzzy numbers. Mathematica Slovaca, 45(3), 269-273.

[16]. Nuray, F., Ulusu, U., & Dündar, E. (2016). Lacunary statistical convergence of double sequences of sets. Soft Computing, 20(7), 2883-2888.

[17]. Pringsheim, A. (1900). Zur theorie der zweifach unendlichen Zahlenfolgen. Mathematische Annalen, 53(3), 289-321.

[18]. Rath, D., & Tripathy, B. C. (1994). On statistically convergent and statistically Cauchy sequences. Indian Journal of Pure and Applied Mathematics, 25, 381-386.

[19]. Reddy, B. S. & Srinivas, M. (2015). Statistically convergent in fuzzy n-normed spaces. Int. J. of Pure and App. Math., 104 , 29-42.

[20]. Šalát, T. (1980). On statistically convergent sequences of real numbers. Mathematica Slovaca, 30(2), 139-150.

[21]. Savaş, E. (2001). On statistically convergent sequences of fuzzy numbers. Information Sciences, 137(1-4), 277-282.

[22]. Schoenberg, I. J. (1959). The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66(5), 361-375.

[23]. Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique. In Colloq. Math, 2(1), 73-74.

[24]. Sencimen, C., & Pehlivan, S. (2008). Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems, 159(3), 361-370.

[25]. Turkmen, M. R., & Dündar, E. (2018). On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces. Journal of Intelligent & Fuzzy Systems (Preprint), pp.1-8. DOI: 10.3233/JIFS-18841

[26]. Turkmen, M. R., & Cinar, M. (2018). Lambda Statistical Convergence in Fuzzy Normed Linear Spaces. Journal of Intelligent and Fuzzy Systems, 34 (6), 4023-4030.

[27]. Turkmen, M. R., & Cinar, M. (2017). Lacunary Statistical Convergence in Fuzzy Normed Linear Spaces. Applied and Computational Mathematics, 6(5), 233-237.

[28]. Turkmen, M. R., & Efe, H. (2013). On some properties of closability of farthest point maps in fuzzy N-normed spaces. i-manager's Journal on Mathematics, 2(4), 33-38.

[29]. Zadeh, L. A. (1965). Fuzzy sets. Inform. Contr., 8(3) , 338-353.

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Research Paper

Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics

James Edward Osler II*

Associate Professor, Department of Allied Professions, North Carolina Central University, USA.

Osler, J. E., II. (2018). Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics, i-manager's Journal on Mathematics, 7(3), 10-29. https://doi.org/10.26634/jmat.7.3.15190

Abstract

This discourse provides a deeper epistemological rational for the novel discipline of “Trioinformatics” through the use of “Trioengineering” to create innovative research instrumentation from trichotomous research questions. Trioengineering uses of the novel mathematical “Ambitation” from “Neuromathematical Neuroengineering Notation” in Trioengineering as a novel operational methodology referred to as “Interapplication”. This specialized operation was first defined in the Trioinformatics article that appeared in the March-May i-manager Journal on Circuits and Systems. Trioengineering's use of the neuromathematics “Ambitation” as an “Interapplication” is the holistic, collaborative, and comprehensive expression of Trioinformatics as a sequential sequence of inquiry into a precise research analysis methodology. Neuroengineering is an innovative way of explaining the transition from trichotomous logic (Osler, 2015) into a trichotomous Triple-I (Osler, 2013d) in which research questions are implemented in a meticulously defined and mathematically associated instrument [first introduced in the i-manager Journal on Mathematics as a part of the Tri- Squared Test (Osler, 2012a)]. Trioinformatics is an in-depth way of symbolically illustrating the law of trichotomy as a mathematically-grounded rational technique for explaining the ternary nature of electronic circuitry (Osler, 2015). The use of the Trioinformatics also adds value to investigative inquiry through the efficacy of digital instruments and tools via eduscientifically - engineered (Osler, 2013) research designs (Osler, 2015).

References

[1]. American Academy of Neurology (AAN). (2012). Working with your doctor. American Academy of Neurology. Retrieved 28 October 2012 from http://patients.aan.com/go/workingwithyourdoctor

[2]. Apostol, T. M. (1967). Calculus, One-variable calculus, with an Introduction to Linear Algebra second edition, Volume one. Waltham, MA: Blaisdell.

[3]. Atta, H. M. (1999). Edwin Smith Surgical papyrus: The oldest known surgical treatise. American Surgeon, 65(12), 1190- 1192.

[4]. Boolos, G., Burgess, J. P., & Jeffrey, R. C. (2002). Computability and Logic. Cambridge University Press.

[5]. Brain Age. (2006). Nintendo Company of America. Based on the work of Ryuta Kawashima, M.D.

[6]. Careersinpsychology. (2015). Retrieved on August 19, 2015 from http://careersinpsychology.org/becoming-aneuropsychologist/

[7]. Carrero, M. (2011). One vital organ: Heart is more than a pump. The Morning Call. Retrieved on February 12, 2011: http://articles.mcall.com/2011-02-12/health/mc-health-neurocardiology-20110212_1_heart-disease-united-states

[8]. Cherry, K. (2014). What is cognition? About Education. Retrieved from http://psychology.about.com/od/cindex/g/ def_cognition.htm

[9]. Cobarrubias, S. (2014). What is neuroplasticity? - Definition, Depression & Quiz. Education Portal. Retrieved from http://education-portal.com/academy/lesson/what-is-neuroplasticity-definition-depression-quiz.html

[10]. Eagleman, D. M. (2011). The brain on trial. July-August 2011, The Atlantic.

[11]. Enderton, H., & Enderton, H. B. (2001). A Mathematical Introduction to Logic. Academic Press.

[12]. Ferreirós, J. (2001). The road to modern logic-an interpretation. Bulletin of Symbolic Logic, 7(04), 441-484.

[13]. Feidakis, M., & Daradoumis, T. (2013). A framework for designing computer supported learning systems with sensibility. International Journal of e-Collaboration, 9(1), 57-70.

[14]. Green, K. J. (1998). Schizophrenia from a Neurocognitive Perspective. Boston, Allyn and Bacon.

[15]. Hidden Curriculum. (2014). In S. Abbott (Ed.), The Glossary of Education Reform. Retrieved from http://edglossary.org/ hidden-curriculum

[16].Hunter, G. (1973). Metalogic: An Introduction to the Metatheory of Standard First Order Logic, (Vol. 294). University of California Press.

[17]. Mandal, A. (2014). What is neurogenesis? Retrieved from http://www.news-medical.net/health/Neurogenesis-What-is- Neurogenesis.aspx

[18]. Mendelson, E. (2009). Introduction to Mathematical logic. CRC Press.

[19]. Natelson, B. H. (1985). Neurocardiology: An interdisciplinary area for the 80s. Archives of Neurology, 42(2), 178-184.

[20]. Neuroscience. (1963). In Merriam-Webster (online). Retrieved from http://www.merriam-webster.com/dictionary/ neuroscience

[21]. Nouri, A. & Mehrmohammadi, M. (2012). Defining the Boundaries for Neuroeducation as a Field of Study. Educational Research Journal, 27(1 & 2).

[22]. Osler, J. E. (2010). Visualus™ Visioneering Volumetrically: The Mathematics of the Innovative Problem-solving Model of Inventive Instructional Design (First Edition). Lulu Publishing, Morrisville NC.

[23]. Osler, J. E. (2012). Trichotomy-Squared – A novel mixed methods test and research procedure designed to analyze, transform, and compare qualitative and quantitative data for education scientists who are administrators, practitioners, teachers, and technologists. i-manager's Journal on Mathematics, 1(3), 23-31.

[24]. Osler, J. E. (2013a). The psychometrics of educational science: Designing trichotomous inventive investigative instruments for qualitative and quantitative for inquiry. i-manager's Journal on Educational Psychology, 8 (3), 15-22.

[25]. Osler, J. E. (2013b). The psychological efficacy of education as a science through personal, professional, and contextual inquiry of the affective learning domain. i-manager's Journal on Educational Psychology, 6 (4), 36-41.

[26]. Osler, J. E. (2013c). Proximal positive parallel notation: A novel method of expressing mathematical complements, collaborations, and combinations. i-manager's Journal on Mathematics, 2 (4), 21-31.

[27]. Osler, J. E. (2013d). Transformational research engineering: Research design metrics for in-depth and empowering k-12 teacher professional development. i-manager's Journal on School Educational Technology, 9 (1), 43-60.

[28]. Osler, J. E. (2014). Triostatistics: The application of innovative in–depth advanced post hoc statistical metrics for the assessment and analysis of statistically significant tri-squared test outcomes. Kentucky Journal of Excellence in College Teaching and Learning, 12(3), 27-39.

[29]. Osler, J. E. (2015). Trioinformatics: The innovative and novel logic notation that defines, explains, and expresses the rational application of the law of trichotomy for digital instrumentation and circuit design. i-manager's Journal on Circuits and Systems, 3(2), 1-7.

[30]. Petoft, A. (2015). Neurolaw: A brief introduction. Iranian Journal of Neurology, 14(1), 53-58.

[31]. Posner, M. I. & Digirolamo, G. J. (2000). Cognitive neuroscience: Origins and promise. Psychological Bulletin, 126(6), 873-889.

[32]. Research Network on Law and Neuroscience (2014). Neurolaw. Retrieved from http://www.lawneuro.org/

[33]. Rust, J. & Golombok, S. (1989). Modern Psychometrics: The Science of Psychological Assessment (2 edition). Florence, KY, US: Taylor & Frances/Routledge.

[34]. Sabitzer, B. (2011). Neurodidactics - A New Stimulus in ICT and Computer Science Education. INTED, 5881-5889.

[35]. Sensagent. (2012). Online Dictionary: www.sensagent.com: Retrieved on May 9, 2012: http://dictionary.sensagent.com/ trichotomy+(mathematics)/en–en/

[36]. Shoenfield, J., & Monk, J. D. (2001). REVIEWS-Mathematical logic.

[37]. Singh, S. (1997). Fermat's Last Theorem. Fourth Estate.

[38]. UC-Berkeley Molecular and Cell Biology Department (2014). Neurobiology. Retrieved from https://mcb.berkeley.edu/ undergrad/major/major-requirements/neuro

[39]. Van der Wall, E. E., & Van Gilst, W. H. (2013). Neurocardiology: Close interaction between heart and brain. Netherlands Heart Journal, 21(2), 51-52.

[40]. Yale University (2010). Cognitive Science. Retrieved from http://www.yale.edu/cogsci/

[41]. Yudofsky, S. C. & Hales, E. H. (2002). Neuropsychiatry and the Future of Psychiatry and Neurology. American Journal of Psychiatry, 159(8), 1261-1264.

[42]. Zymo Research. (2014). What is Epigenetics? Retrieved from http://www.zymoresearch.com/learning-center/ epigenetics/what-is-epigenetics

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Research Paper

Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression

Solomon Kalayu Mengesha* , Gebregewergis Alemu Gebremedhn, Tilahun Ferede*, Cheru Atsmegiorgis ****

-Lecturer, Adigrat University, Tigray, Ethiopia.

-****Hawassa University, Awassa, Ethiopia.

Mengesha, S. K., Gebremedhn, G. A., Tilahun, F., & Atsmegiorgis, C. (2018). Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression, i-manager's Journal on Mathematics, 7(3), 30-41. https://doi.org/10.26634/jmat.7.3.14988

Abstract

Although remarkable progress has been made in the control of the global Human Immunodeficiency Virus (HIV/AIDS) epidemic, the burden of HIV has reached contemporary at the shocking level in Sub-Saharan Africa. Understanding the cycle of HIV/AIDS disease progression can have great value on the effectiveness of the therapy. The purpose of this study is to determine factors affecting the progression between different stages of the disease and to model the progression of HIV/AIDS disease of an HIV infected patients under ART follow-up using multistate Semi-Markov model. A cohort of 526 HIV infected patients has been sampled from a Hawassa University Referral Hospital, Hawassa, Ethiopia, who have been under ART follow up from September 2012 to August 2017. States of the Markovian process are defined by the seriousness of the sickness based on the CD4 counts in cells/microliter. The five states of HIV/AIDS disease progression considered in the multi-state Semi-Markov model were defined based on of the following CD4 cell counts. State I, State II, State III, State IV and Death state. The major transiently prognostic factors between different states of HIV/AIDS disease were sex, age, ART adherence level, TB status, functional status, opportunistic infections , and body weight of patients. Hence, the progression of HIV/AIDS was significantly accelerated with poor ART adherence, patient's co-infection with TB, older patients, and patients being bedridden. The conditional probabilities of patients from any good states to worst state are increasing over time. Weibull sojourn time distribution is the appropriate and is preferably used as sojourn time distribution under multistate models. As time elapsed, the transition probability of patients is more likely to be in worse state than to be in better one. This shows that patients should aware the need to initiate therapy at early stages of the virus.

References

[1]. Asena, T. F., & Goshu, A. T. (2017). Comparison of Sojourn Time Distributions in Modeling HIV/AIDS Disease Progression. Biometrical Letters, 54(2), 155-174.

[2]. Cochran, W. G. (1977). Sampling Techniques (3 Ed.) New York: John Wiley & Sons Inc.

[3]. Desalegn, P. (2016). Statistical Analysis of Adult HIV/AIDS Patients and Modeling of AIDS Disease Progression. Science Journal of Applied Mathematics and Statistics, 4(5), 189-201.

[4]. Dinberu, S., Kibralem, S., Sisay, W. & Mulualem, T. (2016). Predicting AIDS disease progression using Longitudinal CD4 count among Adult HIV/AIDS Patients in Southwest Ethiopia: Application of Semi- Markov process. International Journal of Computational Bioinformatics and In Silico Modeling, 5(2), 808-814.

[5]. Egerö, B. & Hammarskjöld, M. (2000). HIV/AIDS in the World Today a Summary of Trends and Demographic Implications. Swedish International Development Cooperation Agency, Health Division Document, 2000(1), 1-23.

[6]. Federal Democratic Republic of Ethiopia Ministry of Health (2014). National Guidelines for Comprehensive HIV Prevention, Care and Treatment. Retrieved from https://aidsfree.usaid.gov/sites/default/files/ethiopia_natl_gl_2014.pdf

[7]. Foucher, Y., Mathieu, E., Saint-Pierre, P., Durand, J. F., & Daurès, J. P. (2005). A Semi-Markov Model based on Generalized Weibull Distribution with an Illustration for HIV Disease. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 47(6), 825-833.

[8]. Goshu, A. T., & Dessie, Z. G. (2013). Modelling progression of HIV/AIDS disease stages using semi-Markov processes. Journal of Data Science, 11(2), 269-280.

[9]. Grover, G., Gadpayle, A. K., Swain, P. K., & Deka, B. (2013). A multistate Markov Model based on CD4 Cell Count for HIV/AIDS patients on Antiretroviral Therapy (ART). International Journal of Statistics in Medical Research, 2, 144-151.

[10]. Krol & Saint-Pierre. (2015). SemiMarkov: An R Package for Parametric Estimation in Multi-State Semi-Markov Models. Journal of Statistical Software, 66(6), 1-16.

[11]. Mwambura, S., & Samuel, K. (2017). Generation of Mean Transition (Sojourn) Time in Transient States of HIV Disease Progression in Kenya. International Journal of Social Science and Humanities Research, 5(2), 734-739.

[12]. PEFPAR. (2016). Ethiopia Small Grants Programme Guidelines and Application Form. Ethiopian and American in Partnership to Fight HIV/AIDS (pp. 2-16).

[13]. Reddy, T. (2011). The Application of Multistate Markov Models to HIV Disease Progression (Doctoral Dissertation, University of KwaZulu-Natal, Westville).

[14]. Sharp, P. M., & Hahn, B. H. (2011). Origins of HIV and the AIDS pandemic. Cold Spring Harbor Perspectives in Medicine, 1(1), a006841.

[15]. UNAIDS. (2017). World AIDS Day 2017 [Fact Sheet]. Global HIV statistics.

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Research Paper

An Inventory Model for Two Storage System with Stock Dependent Demand

Amit Kumar Attri* , S. R. Singh, Shweta Choudhary*

* Assistant Professor, Department of Mathematics, Delhi Technical Campus, Greater Noida, Uttar Pradesh, India.

Professor, Department of Mathematics, CCS University Meerut, Uttar Pradesh, India.

* Associate Professor and Head, Department of Applied Sciences, ABES Engineering College,.Dr. A. P. J. Abdul Kalam Technical University, Ghaziabad, Uttar Pradesh, India.

Attri, A. K., Singh, S. R., & Choudhary, S. (2018). An Inventory Model for Two Storage System with Stock Dependent Demand, i-manager's Journal on Mathematics, 7(3), 42-50. https://doi.org/10.26634/jmat.7.3.14668

Abstract

In this paper an inventory model to find out the buyer's optimal policy with two storage system has been developed. The buyer purchases a lot of Q units and transfers this stock in the display area in n equal lots. The demand considered here is a function of displayed stock level. The objective of this model is to optimize the total average cost for the buyer and find out the optimal number of shipments. A numerical example is presented to illustrate this study. The sensitivity analysis presented here shows that the model is quite stable and reflects the real life marketing situations.

References

[1]. Baker, R. A., & Urban, T. L. (1988). A deterministic inventory system with an inventory-level-dependent demand rate. Journal of the Operational Research Society, 39(9), 823-831.

[2]. Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5(4), 323-326.

[3]. Datta, T., & Pal, A. (1990). A Note on an Inventory Model with Inventory-Level-Dependent Demand Rate. The Journal of the Operational Research Society, 41(10), 971-975. doi:10.2307/2583275.

[4]. Ghare P. M., & Schrader G. F. (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering, 14, 238-243.

[5]. Goswami, A., & Chaudhuri, K. S. (1992). An economic order quantity model for items with two levels of storage for a linear trend in demand. Journal of the Operational Research Society, 43(2), 157-167.

[6]. Hartely V. R. (1976). Operations Research - A Managerial Emphasis, Good Year Publishing Company, California.

[7]. Kang, S., & Kim, I. T. (1983). A study on the price and production level of the deteriorating inventory system. International Journal of Production Research, 21, 449-460.

[8]. Kar, S., Bhunia, A. K., & Maiti, M. (2001). Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon. Computers & Operations Research, 28(13), 1315-1331.

[9]. Khurana, D., Pundir, S. R., & Tayal. (2015). A Supply Chain Production Inventory Model for Deteriorationg Product with Stock Dependent Demand under Inflationary Environment and Partial Backlogging. International Journal of Computer Applications, 131(1), 6-12.

[10]. Kumar, N., & Singh, S. R. (2009). Two-warehouse inventory model with stock-dependent demand for deteriorating items with shortages., The IUP Journal of Computational Mathematics, 2(3), 7-23.

[11]. Maity, K., & Maiti, M. (2005). Production inventory system for deteriorating multi-item with inventory-dependent dynamic demands under inflation and discounting. Tamsui Oxford Journal of Management Science, 21(1), 1-18.

[12]. Mandal, B. A., & Phaujdar, S. (1989). An inventory model for deteriorating items and stock-dependent consumption rate. Journal of the Operational Research Society, 40(5), 483-488.

[13]. Sarker, B. R., Mukherjee, S., & Balan, C. V. (1997). An order-level lot size inventory model with inventory-level dependent demand and deterioration. International Journal of Production Economics, 48(3), 227-236.

[14]. Sarma, K. V. S. (1983). A deterministic inventory model with two levels of storage and an optimal release rule. Opsearch, 20, 175-180.

[15]. Singh, S. R., Kumar, N., & Kumari, R. (2008). Two-Warehouse inventory model for deteriorating items with partial backlogging under the conditions of permissible delay in payments. International Transactions in Mathematical Sciences & Computer, 1(1), 123-134.

[16]. Singh, S. R., Rastogi, M., & Tayal, S (2015). A supply chain production inventory model for deteriorating product with stock dependent demand under inflationary environment and partial backlogging. International Journal of Computer Applications, 131 (1), 6-12.

[17]. Singh, S., Khurana, D., & Tayal, S. (2016a). An economic order quantity model for deteriorating products having stock dependent demand with trade credit period and preservation technology. Uncertain Supply Chain Management, 4(1), 29- 42.

[18]. Singh, S. R., Rastogi, M., & Tayal, S. (2016b). An inventory model for deteriorating items having seasonal and stockdependent demand with allowable shortages. In Proceedings of Fifth International Conference on Soft Computing for Problem Solving, pp. 501-513, Springer, Singapore.

[19]. Tayal, S., Singh, S. R., Chauhan, A., & Sharma, R. (2014a). A deteriorating production inventory problem with space restriction. Journal of Information and Optimization Sciences, 35(3), 203-229.

[20]. Tayal, S., Singh, S. R., Sharma, R., & Chauhan, A. (2014b). Two echelon supply chain model for deteriorating items with effective investment in preservation technology. International Journal of Mathematics in Operational Research, 6(1), 84- 105.

[21]. Tayal, S., Singh, S., & Sharma, R. (2015a). An inventory model for deteriorating items with seasonal products and an option of an alternative market. Uncertain Supply Chain Management, 3(1), 69-86.

[22]. Tayal, S., Singh, S. R., Sharma, R., & Singh, A. P. (2015b). An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate. International Journal of Operational Research, 23(2), 145- 162.

[23]. Wee, H. M. (1995). Joint pricing and replenishment policy for deteriorating inventory with declining market. International Journal of Production Economics, 40(2-3), 163-171.

[24]. Wu, K. S., Ouyang, L. Y., & Yang, C. T. (2006). An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. International Journal of Production Economics, 101(2), 369-384.

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Research Paper

Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings

Apurva Kumar Das* , Shailesh Dhar Diwan, Swati Jain*

* Lecturer, Department of Mathematics, Government Polytechnic College Sukma, Chhattisgarh, India.

Associate Professor and Head, Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

* Assistant Professor and Head, Department of Computer Science, Government J. Yoganandam Chhattisgarh College, Raipur, Chhattisgarh, India.

Das, A. K., Diwan, S. D., & Jain, S. (2018). Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings, i-manager's Journal on Mathematics, 7(3), 51-60. https://doi.org/10.26634/jmat.7.3.15064

Abstract

The purpose of this paper is to introduce multivalued version of CR iteration process given by Chugh, Kumar, and Kumar (2012) and provecommon fixed point theorem for this iteration in three multivalued ρ-nonexpansive mappings in modular space. Let ρϵη satisfy (UUC1) and C ⊂ L_pbe nonempty ρ-bounded and convex set. Let T₁, T₂, T₃: C →P_ρ(C) be three multivalued mappings such that P^T1_ρ, P^T2_ρ and P^T3_ρ are ρ-nonexpansive mappings with F = F_ρ(T₁) ⋂ F_ρ(T₂) ⋂ F_ρ(T₃) ≠ φ. Suppose T₁ , T₂ and T₃ satisfy condition (I). Then the sequence {f_n} defined by us converges to a point of F.

References

[1]. Abdou, A. A. N., Khamsi, M. A., & Khan, A. R. (2014). Convergence of Ishikawa iterates of two mappings in modular function spaces. Fixed Point Theory and Applications, 2014(74), 1-10.

[2]. Chugh, R., Kumar, V., & Kumar, S. (2012). Strong convergence of a new three step iterative scheme in Banach spaces. American Journal of Computational Mathematics, 2(4), 345-357.

[3]. Dehaish, B. A. B., & Kozlowski, W. M. (2012). Fixed point iteration processes for asymptotic pointwise nonexpansive mapping in modular function spaces. Fixed Point Theory and Applications, 2012(118), 1-23.

[4]. Dhompongsa, S., Domínguez Benavides, T., Kaewcharoen, A., & Panyanak, B. (2006). Fixed point theorems for multivalued mappings in modular function spaces. Scientiae Mathematicae Japonicae, e-2006, 139-147.

[5]. Ishikawa, S. (1974). Fixed points by a new iteration method. Proceedings of the American Mathematical Society, 44(1), 147-150.

[6]. Kassu, W. W., Sangago, M.G., & Zegeye, H. (2016). Approximating the common fixed point of two multivalued mappings by Ishikawa iterates in modular function spaces. Int. J. Nonlinear Anal. Appl. (submitted).

[7]. Khamsi, M.A., & Kozlowski W.M. (2011). On asymptotic pointwise nonexpansive mappings in modular function spaces. Journal of Mathematical Analysis and Applications, 380(2), 697-708.

[8]. Khamsi, M.A., Kozlowski, W.M., & Reich, S. (1990). Fixed point theory in modular function spaces. Nonlinear Analysis, 14(11), 935-953.

[9]. Khan, S.H., & Abbas, M. (2014). Approximating the fixed points of multivalued ρ-nonexpansive mappings in modular function spaces. Fixed Point Theory Applications, 2014(34).

[10]. Kozlowski, W. M. (1988). Modular Function Spaces. Series of Monographs and Textbooks in Pure and Applied Mathematics, (vol. 122). Marcel Dekka, New York, USA.

[11]. Kutib, M.A., & Latif A. (2009). Fixed points of multivalued mappings in modular function spaces. Fixed Point Theory Applications, 2009, 1-12.

[12]. Mann, W. R. (1953). Mean value methods in iteration. Proceedings of the American Mathematical Society (Vol. 44, pp., 506-510).

[13]. Musielak, J., & Orlicz, W. (1959). On modular spaces. Studia Mathematica, 18(1), 49-65.

[14]. Markin, J. T. (1968). A fixed point theorem for set valued mappings. Bulletin of the American Mathematical Society, 74(4), 639-640.

[15]. Nadler, S. B. (1969). Multi-valued contraction mappings. Pacific Journal of Mathematics, 30(2), 475-488.

[16]. Nakano, H. (1950). Modulared Semi-Ordered Linear Spaces. Maruzen Co.

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