Bipolar metric spaces and some fixed point theorems

Abstract

In this paper we introduce the concept of bipolar metric space as a type of partial distance. We explore the link between metric spaces and bipolar metric spaces, especially in the context of completeness, and prove some extensions of known fixed point theorems.

Some fixed point theorems in fuzzy bipolar metric spaces

“…Numerous of generalizations of metric space have been introduced by many eminent mathematicians. Recently, Mutlu and Gurdal [9] generalized metric space which was called bipolar metric spaces and give a new concept of measurement of distance between the elements of two different sets as: 9]). The 3-tuple (X, Y, d) is said to a bipolar metric space if X and Y are two nonempty sets and d is a function on defined on X × Y to R + , where R + denotes the set of nonnegative real numbers, satisfying following properties:…”

Some Applications via Common Coupled Fixed Point Theorems in Bipolar Metric Spaces

“…Subsequently, many authors established coupled fixed point theorems in different spaces (see [4]- [13]). This work is motivated by the recent work on extension of Banach contraction principle on Bipolar metric spaces, which has been done by Mutlu and Gu¨rdal [14]. Also, they investigated some fixed point and coupled fixed point results on this spaces (see [14], [15]).…”

Caristi type cyclic contraction and common fixed point theorems in bipolar metric spaces with applications

“…One of the recently popular topics in fixed point theory is addressing the existence of fixed points of contraction mappings in bipolar metric spaces, which can be considered as generalizations of the Banach contraction principle. In 2016, Mutlu and Gürdal [1] have introduced the concepts of bipolar metric space and they investigated certain basic fixed point and coupled fixed point theorems for covariant and contravariant maps under contractive conditions; see [1,2].…”

“…Also, we give examples and applications to homotopy theory and integral equations. d(b, a), for all a, b ∈ A ∩ B, (B 3 ) d(a 1 , b 2 ) ≤ d(a 1 , b 1 ) + d(a 2 , b 1 ) + d(a 2 , b 2 ), for all a 1 , a 2 ∈ A, b 1…”