Integral Equations in Two Variables

Abstract

Integral equations in two and more variables have been treated by many investigators and various methods have been proposed for the study of different aspects of their solutions. This intensively investigated area is in a process of continuous development, reflected in the great number of books and papers dedicated to it, see [5–10,13–18,20,23–27,33,34,36,38–45,49,50,52–55,59–66,68,74–140] and the references cited therein. Nevertheless, there are still many aspects related to certain such equations, which we believe need to be enlightened. In response to the growing use of such equations in many applications, in this chapter we study some important qualitative properties of solutions of certain integral and integrodifferential equations in two variables. The fundamental tools employed in the analysis are based on applications of the Banach fixed point theorem and certain recent integral inequalities with explicit estimates on the unknown functions.