On the Solvability of a Class of Nonlinear Integral Equations in Hölder Spaces

Abstract

In this paper, using the classical Schauder fixed point theorem, we prove that a nonlinear class of integral equations has at least one solution in the space of functions satisfying the Hölder condition. Also, some important examples showing the applicability of the existence theorem presented in this study are given.

Keywords:

• Nonlinear integral equation
• Hölder spaces
• Schauder fixed point theorem

2000 Mathematics Subject Classification:

• 45G10
• 45M99
• 47H10