Geraghty Type Contraction and Common Coupled Fixed Point Theorems in Bipolar Metric Spaces with Applications to Homotopy

Abstract

In this paper, we establish the existence of common coupled fixed point results of two covariant mappings in a complete bipolar metric spaces under Geraghty type contraction by using weakly compatible mappings with an example. We have also provided an applications to Homotopy theory.

The common fixed points in a bipolar metric space

“…The purpose of this paper is to obtain a fixed point theorem in the bipolar metric spaces (see [2,15,16,20,21,22]). The contraction condition used in our theorem is the extension of Boyd-Wong (see [4]) in bipolar metric spaces.…”

Common Fixed Point for Meir–Keeler Type Contraction in Bipolar Metric Space

“…The response of the researchers resulted in various types of metrics, such as the cone metric, the partially ordered metric, the modular metric, and more recently the complex-valued metrics proposed by Huang and Zhang [6], Matthew [7], Azam et al [8], and Murthy et al [9]. For more details on the topic, see [10][11][12][13][14][15][16]) and the references therein.…”

Some common fixed point theorems in bipolar metric spaces and applications

“…Also, this new notion of generalization and improvement of a metric space leads to the existence and the development of fixed point theorems. However, in bipolar metric spaces, a lot of significant work has been done to the existence for a fixed point of various mappings (see [7], [9], [10], [17]) and references therein). Recently, Kishore et al [8] obtained some common fixed point theorems in bipolar metric spaces along with some applications, while Mutlu [14] extended the Banach fixed point theorem and the result due to Kannan [5] in bipolar metric spaces.…”