Weak convergence of fixed point iterations in $S$-metric spaces

Abstract

This paper extends the notion of weak convergence in metric spaces to the case of S-metric spaces. Moreover, some results on the weak convergence of fixed point iterations of Banach's, Kannan's, Chatterjee's, Reich's, Hardy and Roger's types of contractions on S-metric spaces are obtained. In addition, an example is presented to demonstrate our primary result.

Keywords

• weak convergence
• semi s-metric space
• directed set