Abstract
In this paper, we introduced the concept of (α, β)-admissible Geraghty type contractive mappings. Sufficient conditions for the existence of a fixed point for such class of generalized nonlinear contractive mappings in metric spaces are provided. As applications, we derive a fixed point theorem for these contractions whenever the space is endowed with a graph. Some interesting consequences of our theorems are also obtained. The proved results generalize and extend various well-known results in the literature. Some examples are illustrated for the usability of the results.
Highlights
Introduction and preliminariesFixed point theory has gained very large impetus due its wide range of applications in various fields such as engineering, economics, computer science, and many others
It is well known that the contractive-type conditions are very indispensable in the study of fixed point theory and Banach’s fixed point theorem [1] for contraction mappings & Sumit Chandok chansok.s@gmail.com
In 2012, Samet et al [15] introduced the concepts of acontractive and a-admissible mappings and established various fixed point theorems for such class of mappings defined on complete metric spaces
Summary
Some fixed point theorems for (a, b)-admissible Geraghty type contractive mappings and related results. This article is published with open access at Springerlink.com
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