Δ−Convergence Theorems for Multivalued Non-expansive Mappings in Hyperbolic Spaces

Xian-Cai Lei

doi:10.4172/2168-9679.1000158

Abstract

The purpose of this paper is that iteration scheme of multivalued non-expansive mappings in Banach spaces is extended to hyperbolic spaces and to prove some Δ−convergence theorems of the mixed type iteration process to approximating a common fixed point for two multivalued non-expansive mappings and two non-expansive mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.

Highlights

The study for fixed point problem involve that multivalued contractions and non-expansive mappings used the Hausdorff metric was initiated by Markin [1,2] later, different iterative processes have used to approximate the fixed points of multivalued non-expansive mappings in Banach space, many scholars have made extensive research in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
The hyperbolic space has no set up the theory of multivalued non-expansive mappings fixed point
In order to define the concept of multivalued non-expansive mapping in the general setup of Banach spaces, we first collect some basic concepts

Summary

Introduction

The study for fixed point problem involve that multivalued contractions and non-expansive mappings used the Hausdorff metric was initiated by Markin [1,2] later, different iterative processes have used to approximate the fixed points of multivalued non-expansive mappings in Banach space, many scholars have made extensive research in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. The hyperbolic space has no set up the theory of multivalued non-expansive mappings fixed point. Lemma 1.3: [26] Let (X, d, W) be a complete uniformly convex hyperbolic space with monotone modulus of uniform convexity.

Objectives

Results

Conclusion