Fixed points of generalized $alpha$-Meir-Keeler type contractions and Meir-Keeler contractions through rational expression in $b$-metric-like spaces

Abstract

In this paper, we first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.