Cone S-metric spaces and some new fixed point results for contractive mapping satisfying $\phi$-maps with implicit relation

Abstract

In this article, we use implicit relations to establish some new fixed point results in the setting of cone S-Metric spaces for phi-map type contractive conditions. An example is provided to support our results. Our results extend, unify, and generalize several results from the current literature. In particular, the results presented in this paper improve and generalize the corresponding results of Sedghi and Dung[8], which used the ideas of Saluja, G. S. [19].