Nonlinear equations of Hammerstein-Volterra type in the space of functions of bounded k-variation in the sense of Korenblum.

Abstract

In this paper we study some nonlinear integral equations and give conditions for the functions and kernel involved in such equations under which we assure the existence, uniqueness, and continuity of solutions in the space of functions of bounded $\kappa$-variation in the sense of Korenblum, $(\kappa BV\left([a,b]\right))$.