On the Existence of the Solutions of A Nonlinear Fredholm Integral Equation in Hölder Spaces

Year 2022, Volume: 10 Issue: 1, 16 - 26, 01.03.2022

Merve Temizer Ersoy

https://doi.org/10.36753/mathenot.756916

Cited By: 1

Abstract

In this article, we prove the theorem concerning the existence of the solutions for some nonlinear integral equations. As an application, we investigate the problem of existence of solutions of Fredholm integral equations using the technique of relative compactness in conjunction with fixed point theorem. Our solutions are placed in the space of functions satisfying the Hölder condition. Our work is more general than the previous works in [1-3]. In the last section, we show the efficiency of this approach on one numerical example.

Keywords

Hölder condition , Fredholm integral equation , Schauder fixed point theorem

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