Fixed point theorems for multivalued mappings on bipolar metric spaces

Abstract

In this article, we introduce concepts of Pompeiu-Hausdorff bipolar metric, multivalued covariant and contravariant contraction mappings in bipolar metric spaces. In addition to these, we express two main fixed point theorems, which are supported with four important corollaries, related to these multivalued mappings. Finally we give an example which presents the applicability of our obtained results.

Some fixed point theorems in fuzzy bipolar metric spaces

“…The new notions of generalization and improvement of metric spaces leads to give existence and development of fixed point theorems. As in bipolar metric spaces a lot of significant work has been done by researchers (see, [5,[10][11][12]) and in fuzzy metric spaces, Grabeic [2] extend the well known fixed point theorem of Banach to fuzzy metric spaces in the sense of Karamosil and Michalek [6]. After that, Gregori and Sapena [3] extended the fuzzy banach contraction theorem to fuzzy metric space in the sense George and Veeramani's [2].…”

Common Fixed Point Theorems in Bipolar Metric Spaces with Applications to Integral Equations

“…Hence F and G have a unique common fixed point in U ∪V. Remark 2.6: In theorem 2.5, if F=G, (1) where ∈(0, 1). 2In this case, we have the following corollary, which can also be found in [2].…”

“…Very recently, Mutlu and Gürdal [2] introduced notion of bipolar metric spaces in 2016. Also, they investigated some fixed and coupled fixed point results on this space (see, [1] [2]) and reference therein. In this paper, we will continue to study fixed points in the frame of bipolar metric-spaces.…”

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

“…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 Gürdal [1]. Also they investigated some fixed point and coupled fixed point results on this spaces (see [1], [2]). Later, we proved some fixed point theorems in our earlier papers (see [3], [4]).…”