Fixed point and common fixed point theorems on (α,f)-contractive multi-valued mappings in uniform spaces

Abstract

In this paper, we introduce the notion of (?,F)-contractive multi-valued mappings in the setting of uniform spaces. Some fixed point and common fixed point theorems for (?,F)-contractive mappings endowed with the uniform spaces are established. The existence and uniqueness of fixed points by using the structure of uniform spaces is discussed in detail. We set up a non-trivial example for the elaboration of these novel results. eventually, an application is also provided to elaborate the applicability of our results.

Recent Advances in Proximity Point Theory Applied to Fractional Differential Equations

“…Klim et al [19] demonstrated FP theorems involving F -contractions for dynamic processes. In 2022, Sagheer et al [20] developed the concept of (↑, F )-contractive multi-valued mappings on uniform spaces and proved certain fixed-point results. In 2010, Basha [21] introduced the notion of the best proximity point (BPP) for nonself mappings on metric spaces, and subsequent research has explored the existence of BPP for non-self mappings on metric spaces (see for example [22,23]).…”