Fixed point theorems in WC{Banach algebras and their applications to innite systems of integral equations

Abstract

The paper is devoted to prove a few xed point theorems for operators acting in
WC{Banach algebras and satisfying some conditions expressed in terms of a generalized Lipschitz
continuity and measures of weak noncompactness. Moreover, the assumptions imposed on the
mentioned operators are formulated with help of weak topology and weak sequential continuity.
Our xed point results will be illustrated by proving the existence of solutions of an innite system
of nonlinear integral equations.