Some new fixed point theorems for set-valued contractions in complete metric spaces

Chi-Ming Chen

doi:10.1186/1687-1812-2011-72

Abstract

AbstractIn this article, we obtain some new fixed point theorems for set-valued contractions in complete metric spaces. Our results generalize or improve many recent fixed point theorems in the literature.MSC: 47H10, 54C60, 54H25, 55M20.

Highlights

Introduction and preliminariesLet (X, d) be a metric space, D a subset of X and f : D ® X be a map
A mapping f : X ® X is called a quasi-contraction if there exists k < 1 such that d(fx, fy) ≤ k · max{d(x, y), d(x, fx), d(y, fy), d(x, fy), d(y, fx)}
Amini-Harandi [5] gave the following fixed point theorem for setvalued quasi-contraction maps in metric spaces

Summary

Introduction

Introduction and preliminariesLet (X, d) be a metric space, D a subset of X and f : D ® X be a map. In 1974, C’iric’ [2] introduced these maps and proved an existence and uniqueness fixed point theorem. The existence of fixed points for various multi-valued contractive mappings had been studied by many authors under different conditions.

Results

Conclusion