i-manager's Journal on Mathematics (JMAT)


Volume 5 Issue 4 October - December 2016

Research Paper

Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces

T Rakesh Singh* , P Srikanth Rao**
* Associate Professor, Department of Mathematics, Aurora’s Technological Institute, Hyderabad, Telangana, India.
** Professor, Department of Mathematics, B. V. Raju Institute of Technology, Narsapur, Telangana, India.
Singh, T.R., and Rao, P.S. (2016). Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces. i-manager’s Journal on Mathematics, 5(4), 1-10. https://doi.org/10.26634/jmat.5.4.8305

Abstract

A fuzzy set of X is a function with domain X and values in [0, 1]. If A is a fuzzy set and x ? X, then the function values A(x) are called the grade of membership of x in A. A mapping F from X to F(Y) is called a fuzzy mapping if for each x ? X; F(x) is a fuzzy set on Y and F(x)(y) denotes the degree of membership of y in F(x). Let X be a metric linear space and let W(X) denote the set of all fuzzy sets on X such that each of its α-cut is a nonempty compact and convex subset (approximate quantity) of X. A fuzzy mapping F from X to W(X) is called a fuzzy contraction mapping if there exists q ? (0, 1) such that D(F(x), F(y)) ≤ qd(x, y) for each x,y ? X. In this paper, two common coupled fixed point theorems for six self maps is proved under Wcompatible conditions in fuzzy metric spaces. Coupled fixed point and coupled point of coincidence for contractive mappings in complete fuzzy metric space is also obtained. The results obtain an extension of Theorem 2.1 by K. Pandu Ranga Rao, K. Rama Koteswara Rao, and S. Sedghi, (2014) [11]. Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces. Finally, an example has been given to illustrate the usability of the main result.

Research Paper

Modified Maximum Likelihood Estimation: Inverse Half Logistic Distribution

R. Subba Rao* , Pushpa Latha Mamidi**, R. R. L. Kantam***
* Professor, Department of Mathematics, SRKR Engineering College, Bhimavaram, Andhra Pradesh, India.
** Assistant Professor, Department of Mathematics, Vishnu Institute of Technology, Bhimavaram, Andhra Pradesh, India.
*** Retired Professor, Department of Statistics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur, Andhra Pradesh, India.
Rao, R.S., Mamidi, P.L., and Kantam, R.R.L. (2016). Modified Maximum Likelihood Estimation: Inverse Half Logistic Distribution. i-manager’s Journal on Mathematics, 5(4), 11-19. https://doi.org/10.26634/jmat.5.4.8306

Abstract

If a random variable follows a particular distribution, then the distribution of the inverse of that random variable is called inverted distribution. In this paper, the pdf of Inverse Half Logistic Distribution (IHLD) is derived. The mathematical properties of this distribution have been studied. The parameter is estimated from a complete sample using the classical maximum likelihood method. The estimating equations are modified to get simpler and efficient estimators. Two methods of modification are suggested. The sampling characteristics of the modified estimates are also presented for performance comparisons.

Research Paper

Some coupled fixed point theorems in M- fuzzy metric spaces using the common (E.A) property

Dr Pranjali* , Shailesh Dhar Diwan**
* Senior Assistant Professor, Department of Mathematics, Shri Shankaracharya Institute of Prof. Mgmt. and Tech., Raipur (C.G.), India.
** Associate Professor, Department of Mathematics, Government Engineering College, Raipur (C.G.), India.
Sharma, P., and Diwan, S.D. (2016). Some Coupled Fixed Point Theorems in M-Fuzzy Metric Spaces using the Common (E.A.) Property. i-manager’s Journal on Mathematics, 5(4), 20-29. https://doi.org/10.26634/jmat.5.4.8307

Abstract

In this paper, the authors have defined some properties in M-fuzzy metric spaces defined by Sedgi and Shobe [15] and they established some common coupled fixed point theorems in M-fuzzy metric space using an implicit relation. They defined the notion of (E.A.) property and common (E.A.) property for the pair of mappings defined in — fuzzy metric space. The obtained results extend, generalize, and improve several results of D - metric spaces defined by Dhage [3] and metric spaces to generalized fuzzy metric spaces or M-fuzzy metric spaces.

Research Paper

Advanced Tri–Analytic Trichotomous Post Hoc Repeated Measures forTri–Squared Test Inventive Investigative Instrument Items Using Trichotomous Variation Analysis [Trivariant Analysis]

James Edward Osler II*
Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.
Osler, J. E., II. (2016). Advanced Tri–Analytic Trichotomous Post Hoc Repeated Measures for Tri–Squared Test Inventive Investigative Instrument items using Trichotomous Variation Analysis [Trivariant Analysis]. i-manager’s Journal on Mathematics, 5(4), 30-46. https://doi.org/10.26634/jmat.5.4.8308

Abstract

This monograph provides an epistemological rational for the Post Hoc testing of the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test introduced in the Journal on Mathematics, and further detailed in the Journal on Educational Technology, Journal on School Educational Technology, and in Journal on Educational Psychology articles. Advanced statistical measures of internal research instrument Trichotomous Repeated Measures and Trichotomous Variation of significant Transformative Trichotomy–Squared [Tri–Squared] research variables are analyzed. This additional novel approach to advanced Tri–Squared data analysis adds additional value to the mixed methods approach of research design that involves the holistic combination and comparison of qualitative and quantitative data outcomes. Multiple sequential mathematical models are provided that illustrate the entire process of advanced Tri–Analytic inquiry.

Research Paper

Extreme Value Control Chart for Burr Type XII Distribution

M.S. Ravi Kumar* , R. R. L. Kantam**
* Associate Professor, Department of Community Medicine, Konaseema Institute of Medical Sciences & Research Foundation, Amalapuram, Andhra Pradesh, India.
** Retired Professor, Department of Statistics, Acharya Nagarjuna University, Nagarjunanagar, Andhra Pradesh, India.
Ravikumar, M.S., and Kantam, R.R.L. (2016). Extreme Value Control Chart for Burr Type XII Distribution. i-manager’s Journal on Mathematics, 5(4), 47-51. https://doi.org/10.26634/jmat.5.4.8309

Abstract

Variable control charts are based on subgroup statistics and variation in the values of the subgroup statistics between subgroups. In this paper, sampling distribution of extreme order statistics for a given sample from Burr Type XII Distribution are considered and its percentiles are used to develop an extreme value control chart for a process variate. The approximation to Normal Distribution of the Burr Distribution is explored to develop the technique of popular ANalysis Of Means (ANOM) through Burr Distribution. Comparative study of the approximations are made. The results are explained by an illustration.