Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces

Abstract

In this paper, we introduce the concept of multivalued contraction mappings in partially ordered bipolar metric spaces and establish the existence of unique coupled fixed point results for multivalued contractive mapping by using mixed monotone property in partially ordered bipolar metric spaces. Some interesting consequences of our results are obtained.

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.…”

On Two Banach-Type Fixed Points in Bipolar Metric Spaces

“…Finding fixed points for different type of contractions has become the focus of fruitful research activity, and numerous fixed point results in that theory can be found in the literature. Recently, many investigators have published various papers on the fixed point in bipolar metric spaces, and these can be read in [4][5][6][7][8][9][10][11][12][13] and the references therein, just to name a few. Bartwal et al [14] even initiated the concept of fuzzy bipolar metric spaces.…”

α , BK -Contractions in Bipolar Metric Spaces

“…Some basic examples are distance between lines and points in an Euclidean space, distance between points and sets in a metric spaces, affinity between a class of students and a set of activities, lifetime mean distances between people and places, and many more. Many investigators have published various papers on fixed point in bipolar metric spaces, and these can be read in [2][3][4][5][6] and the references therein, just to name a few. is new notion of generalization and improvement of metric spaces leads to give existence and development of fixed-point theorems.…”