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

Volume 7 Issue 3 July - September 2018

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 ⊂ Lp be nonempty ρ-bounded and convex set. Let T1, T2, T3: C →Pρ(C) be three multivalued mappings such that PT1ρ, PT2ρ and PT3ρ are ρ-nonexpansive mappings with F = Fρ(T1) ⋂ Fρ(T2) ⋂ Fρ(T3) ≠ φ. Suppose T1 , T2 and T3 satisfy condition (I). Then the sequence {fn} defined by us converges to a point of F.