Fixed point theorems for N-generalized hybrid mappings in uniformly convex metric spaces

Withun Phuengrattana

doi:10.1186/1687-1812-2013-188

Abstract

In this paper, we prove some fixed point theorems for N-generalized hybrid mappings in both uniformly convex metric spaces and spaces. We also introduce a new iteration method for approximating a fixed point of N-generalized hybrid mappings in spaces and obtain Δ-convergence to a fixed point of N-generalized hybrid mappings in such spaces. Our results improve and extend the corresponding results existing in the literature. MSC:47H09, 47H10.

Highlights

Introduction and preliminaries LetC be a nonempty closed subset of a metric space (X, d) and let T be a mapping of C into itself
We prove a fixed point theorem for N -generalized hybrid mappings in complete uniformly convex metric spaces
Let C be a nonempty closed and convex subset of a complete uniformly convex metric space (X, d, W ) and let T : C → C be an N -generalized hybrid mapping with has a fixed point if and only if there exists an x ∈ C such that {Tnx} is bounded

Summary

Introduction

Introduction and preliminaries LetC be a nonempty closed subset of a metric space (X, d) and let T be a mapping of C into itself. He showed that every nonexpansive mapping defined on a bounded closed convex subset of a complete CAT( ) space always has a fixed point. We prove a fixed point theorem for N -generalized hybrid mappings in complete uniformly convex metric spaces.

Results

Conclusion