Generalized Ulam-Hyers Stability, Well-Posedness, and Limit Shadowing of Fixed Point Problems forα-β-Contraction Mapping in Metric Spaces

Wutiphol Sintunavarat

doi:10.1155/2014/569174

Abstract

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

Highlights

Introduction and PreliminariesThe stability problem of functional equations, first initial from a question of Ulam [1] in 1940, concerns the stability of group homomorphisms
There are a number of results that studied and extended Ulam-Hyers stability for fixed point problems as Bota et al [3], Bota-Boriceanu and Petrusel [4], Brzdek et al [5], Brzdek and Cieplinski [6, 7], Cadariu et al [8], Lazar [9], Rus [10], and F
Afterwards, there are many results about fixed point theorems by using such function in this class in many spaces with different contractions; for details we refer the readers to [25,26,27,28] and references therein

Summary

Introduction

Introduction and PreliminariesThe stability problem of functional equations, first initial from a question of Ulam [1] in 1940, concerns the stability of group homomorphisms. We establish some existence and uniqueness of fixed point theorems for such mappings in metric spaces by using the concept of α-admissible mapping.

Objectives

Results

Conclusion