The Existence of Fixed Point Theorems via w -Distance and α -Admissible Mappings and Applications

Abstract

We introduce the concept of the generalized $w_{\alpha }$-contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of $w$-distance and $\alpha$-admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.