Existence of Solutions to Non-linear Quadratic Integral Equations via Measure of Non-Compactness

TL;DR

This paper investigates the existence of solutions for certain non-linear quadratic integral equations using measure of non-compactness and fixed point theorems in Banach spaces.

Contribution

It introduces fixed point theorems involving measure of non-compactness and applies them to establish solution existence for non-linear quadratic integral equations.

Findings

Existence of solutions established under specific conditions.

Fixed point theorems involving measure of non-compactness proved.

Application to non-linear quadratic integral equations demonstrated.

Abstract

The objective of this manuscript is to enquire for the solvability of a specific type of non-linear quadratic integral equations via the interesting notion of measure of non-compactness. Firstly, we inquire into couple of exciting fixed point theorems involving a measure of non-compactness in the setting of a Banach space. Subsequently, bringing into play a suitable measure of non-compactness and the acquired results, we discuss the existence of solution to the aforementioned kind of non-linear quadratic integral equations.