Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}\left( s\right) $-Metric Spaces

Abstract

In this paper, necessary and sufficient conditions for the existence and uniqueness of fixed points of generalized Geraghty type contraction mappings are given in complete partial $b_{v}(s) $-metric spaces. The results are more general than several results that exist in the literature because of the considered space. A numerical example is given to support the obtained results. Also, the existence and uniqueness of the solutions of an integral equation has been verified considered as an application.

Keywords

• generalized geraghty contraction
• fixed point
• partial $b_{v}left( sright) $ metric spaces
• generalized metric space