Abstract
In this paper, we obtain the existence and uniqueness of the solution for three self mappings in a complete bipolar metric space under a new Caristi type contraction with an example. We also provide applications to homotopy theory and nonlinear integral equations.
Highlights
Fixed point theory plays a vital role in applications of many branches of mathematics
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]
Summary
Fixed point theory plays a vital role in applications of many branches of mathematics. The aim of this paper is to prove the common fixed point results in bipolar metric spaces by using a Caristi type cyclic contraction. Suppose that d : A × B → [0, ∞) is a mapping satisfying the following properties: (B1) d(a, b) = 0 if and only if a = b for all (a, b) ∈ A × B, Kishore et al Fixed Point Theory and Applications (2018) 2018:21 (B2) d(a, b) = d(b, a), for all a, b ∈ A ∩ B, (B3) d(a1, b2) ≤ d(a1, b1) + d(a2, b1) + d(a2, b2), for all a1, a2 ∈ A, b1, b2 ∈ B.
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