CYCLICAL NONLINEAR CONTRACTIVE MAPPINGS FIXED POINT THEOREMS WITH APPLICATION TO INTEGRAL EQUATIONS

CYCLICAL NONLINEAR CONTRACTIVE MAPPINGS FIXED POINT THEOREMS WITH APPLICATION TO INTEGRAL EQUATIONS

M. Al-Khaleel, S. Al-Sharif

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Abstract

In this paper, we present new nonlinear contractions based on altering dis- tances and prove the existence and uniqueness of xed points for cyclic operators. We prove here very interesting xed 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 xed 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.

Keywords

Cyclic operator, nonlinear contraction, xed point theory, integral equation