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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

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