i-manager Publications

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.

Periodicity:July - September'2018
DOI : 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.

Keywords

CR Iteration, Multivalued r- Nonexpansive Mapping, Common Fixed Point, Modular Function Space.

How to Cite this Article?

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

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.

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

Abstract

Keywords

How to Cite this Article?

References

If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Options for accessing this content:

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Pdf	35	35	200	20
Online	35	35	200	15
Pdf & Online	35	35	400	25