Ulam-Hyers Stability and Well-Posedness of Fixed Point Problems forα-λ-Contraction Mapping in Metric Spaces

Marwan Amin Kutbi,Wutiphol Sintunavarat

doi:10.1155/2014/268230

Marwan Amin Kutbi, Wutiphol Sintunavarat

Open Access

https://doi.org/10.1155/2014/268230

Copy DOI

Abstract

We study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized contraction mapping, so calledα-λ-contraction mapping. The results in this paper generalize and unify several results in the literature such as the Banach contraction principle.

Highlights

Introduction and PreliminariesIn 1940, the stability problem of functional equations, first initial from a question of Ulam
We obtain that Theorems 10 and 12 do not claim the uniqueness of fixed point
The fixed point problem x = f (x) is called Ulam-Hyers stable if and only if there exists c > 0 such that, for each ε > 0 and for each w∗ ∈ X called an εsolution of the fixed point equation [41], that is, w∗ satisfies the inequality d (w∗, f (w∗)) ≤ ε, [42]

Summary

Introduction

Introduction and PreliminariesIn 1940, the stability problem of functional equations, first initial from a question of Ulam. We establish some existence and uniqueness of fixed point theorems for such mappings in metric spaces via the concept of α-admissible mapping. Our second purpose is to present Ulam-Hyers stability and well-posedness of a fixed point problem for this mapping in metric spaces.

Objectives

Results

Conclusion