Existence and stability of solutions for a system of quadratic integral equations in Banach algebras

Abstract

The aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo’s fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.

Existence Results for Fractional Integral Equations in Frechet Spaces

“…This significant concept in mathematical science was defined by many authors in different manners [1,2]. In the last years there appeared many papers devoted to the applications of the measure noncompactness for establish some existence and stability results for various types of nonlinear integral equations [3,4]. In some recent works on this subject, authors utilize a new method of a family of measures of noncompactness and fixed point theorems for condensing operators in Fréchet spaces see [5,6].…”