On the solutions of some nonlinear fredholm integral equations in topological Hölder spaces

Abstract

In this article, we show that the existence theorem for fredholm type quadratic integral equation in the space of functions satisfying H¨older the condition, based on the classical Schauder fixed point theorem, has new methods that perform with relative compactness in the H¨older spaces. In section 3, some axioms are introduced to solve the fredholm integral equation. In section 4, one example is presented to verify the effectiveness and applicability of our results.