The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Abstract

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

Keywords

• a measure of noncompactness
• quadruple fixed points
• functional integral equations
• Darbo’s fixed point theorem