Fixed point results with Ω-distance by utilizing simulation functions

Abstract

In this paper, we utilize the concept of simulation functions in sense of Khojasteh et al [10] and the notion of Ω-distance in the sense of Saadati et. al. [1] to introduce the notion of (Ω,\(\mathcal{Z}\))-contraction and (Ω,φ,\(\mathcal{Z}\))-contraction.  We employ our contractions to formulate and prove many fixed point results for Ω-distance.  Our results unify and improve many fixed point results in literature.  Also, we give fixed point results of integral type as well as we support our result by introducing an example.