Fixed point and common fixed point theorems on $(\alpha$,$F)$-contractive multi-valued mappings in uniform spaces.

Abstract

In this paper, we introduce the notion of $(\alpha$,$F)$-contractive multi-valued mapping in the setting of uniform space. We prove some fixed point and common fixed point theorems for $(\alpha$,$F)$-contractive mapping endowed with the uniform space. We demonstrate the existence and uniqueness of fixed points by using the structure of uniform space. We set up some suitable examples for the elaboration of these novel results. An application is also provided to elaborate the applicability of our results.