Cyclical nonlinear contractive mappings fixed point theorems with application to integral equations

Abstract

In this paper, we present new nonlinear contractions based on altering distances and prove the existence and uniqueness of fixed points for cyclic operators. We prove here very interesting fixed point theorems in which we combine and extend the contractive conditions of Banach, Kannan, Chatterjea, and of many others. Our results shall serve as generalized versions of many fixed point results proved in the literature. Examples and application to integral equations that exploits Jensen inequality are given to illustrate the analysis and theory and validate our proved results.