Fixed point theory in a new class of banach algebras and application

Abstract

We introduce a new class of Banach algebras satisfying a certain sequential condition \({(\mathcal{P})}\) and we prove a new variant of fixed-point theorems for the sum and the product of nonlinear sequentially weakly continuous and weakly condensing operators. Later on, as an application, we will give a generalized example of obtained results to prove the existence of solutions of nonlinear integral equation. Our results are formulated in terms of De Blasi measure of weak non-compactness.