On Two Banach-Type Fixed Points in Bipolar Metric Spaces

Abstract

In this article, we propose two Banach-type fixed point theorems on bipolar metric spaces. More specifically, we look at covariant maps between bipolar metric spaces and consider iterates of the map involved. We also propose a generalization of the Banach fixed point result via Caristi-type arguments.

Ciric Type Theorem for Class of Contravariant Functions in Bi-polar Metric Space

“…Since then, numerous investigators have operated on it, developing the findings in various ways. Boyd and Wong [3], Gaba et al [5], Mutlu et al [8], Özkan and Gürdal [9], Rao et al [10], and Siva [13] contributed to the creation of the contraction condition. New spaces including G-metric, cone metric, 2-metric, D-metric, M-metric, fuzzy metric, quasi metric and most recently bi-polar metric space are the focus of several academics (see Bajović et al [1], Mutlu and Gürdal [7], Mutlu et al [8], Rao et al [10,11], and Roy and Saha [12]).…”

Introducing Fixed-Point Theorems and Applications in Fuzzy Bipolar b-Metric Spaces with ψα- and ϝη-Contractive Maps

“…Unlike traditional metric spaces, which focus on distances within a single set, bipolar metric spaces consider distances between points from two distinct sets. Researchers [7,12,13] have since explored fixed-point theorems in bipolar metric spaces, discovering various applications. Building on this, Bartwal et al [14] introduced fuzzy bipolar metric spaces, extending the principles of fuzzy metric spaces.…”

Some generalizations for mixed multivalued mappings

“…This principle is an important tool in the fixed point theory and has been accepted as starting of the fixed point theory in metric spaces. Due to its applicability, many authors have studied to generalize this principle by considering different kinds of contractions or abstract spaces [2,10,11,12,19]. Taking into account multivalued mappings, Nadler [17] proved one of the interesting and famous generalizations of this result in metric spaces as follows:…”