NEW GERAGHTY TYPE CONDENSING OPERATORS AND SOLVABILITY OF NONLINEAR QUADRATIC VOLTERRA-STIELTJES INTEGRAL EQUATION

Abstract

The true motivation of this article is to provide sufficient conditions with the aid of Geraghty type condensing operators that guarantee the existence of a solution of nonlinear quadratic Volterra-Stieltjes integral equation. We also address several new fixed point theorems that ensure the existence of a fixed point for Geraghty type condensing operators in real Banach spaces. An example and numerical approximations are presented to justify the basis of our results.