Common Fixed Point Theorems in Complex-Valued $S$-Metric Spaces via Implicit Relations with Applications

Abstract

The aim of this paper is to present some common fixed point results for four weakly compatible mappings in complex valued $S$-metric spaces. Also, new contraction conditions in this space are given. Finally, as applications of our results, we give the existence and uniqueness of common solution of Hammerstein and Urysohn integral equations.