Relation-preserving generalized nonlinear contractions and related fixed point theorems

Abstract

In this paper, we present some fixed point theorems for generalized nonlinear contractions involving a new pair of auxiliary functions in a metric space endowed with a locally finitely T-transitive binary relation. Our newly proved results generalize some well-known fixed point theorems existing in the literature. We also provide an example which substantiates the utility of our results.

Keywords

• (ϕ，ψ)-contractions
• locally finitely t-transitive binary relations
• r-complete metric space