Two New Geraghty Type Contractions in Gb-Metric Spaces

Abstract

In this work, two Geraghty type contractions are introduced in Gb-metric spaces, and some fixed point theorems about the contractions are proved. At the end of this article, a theorem about unique solution of an integral function is proved.

On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

“…Wang et al [10] obtained the following result by generalizing the result obtained by Karapinar et al [9]. Theorem 1 ([10]).…”

“…In conclusion, following Geraghty [7] and Wang et al [10] we presented a new type of Geraghty contraction and studied fixed point results within the framework of S b -metric space for these contractions which includes auxiliary functions with a restricted co-domain. This new idea of defining Geraghty contraction for self operators generalized a large number of previously published and closely related works for the presence and uniqueness of a fixed point in S b -metric space.…”

“…Numerous authors have dedicated a great deal of attention to Geraghty's results. In metric-like space, Aydi et al [8] examined FP theorems for a new type of Geraghty contractions, Karapinar et al [9] expanded the theory in generalized metric structure, namely b-metric-like-space, Wang et al [10] presented intriguing results pertaining to FP consequences through the notion of Geraghty contraction-type maps in G b −metric spaces, and very recently, Alam et al [11] solved a two-point boundary value problem introducing rational-type Geraghty contraction.…”

“…Following Geraghty [7] and Wang et al [10], we explored new Geraghty types of contractions in the context of S b -metric space. The auxiliary function, which is used to define the first contraction, has a restricted co-domain and a limiting condition that is different from the limiting condition of Geraghty.…”