Coincidence points for graph preserving generalized almost F-G-contractions in b-metric spaces

Abstract

In this paper, we introduce the concept of generalized almost F -G-contraction in a b-metric space endowed with a directed graph G. We prove some new coincidence point results for this type of single-valued and multi-valued mappings in b-metric spaces under some conditions. Our results generalize and extend several well-known comparable results in fixed point theory including Nadler's fixed point theorem for multi-valued mappings. Finally,  some illustrative examples are given to justify the validity of our main result.