New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations

Abstract

We introduce a class of Banach algebras satisfying certain sequential condition (P) and we prove fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators. Later on, we give some examples of applications of these types of results to the existence of solutions of nonlinear integral equations in Banach algebras.

Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

“…The problems of the existence of solutions for an integral equation can then be resolved by searching fixed points for nonlinear operators in a Banach algebra. For this, many researchers have been interested in the case where the Banach algebra is endowed with its strong topology; however, few of them were interested to the existence of a fixed point for mappings acting on a Banach algebra equipped with its weak topology [7][8][9][10][11]; such a topology allows obtaining some generalizations of these results.…”

Measures of Noncompactness in a Banach Algebra and Their Applications

“…[6,7,11,12,18,19]). We will use the technique associated with measures of noncompactness and some fixed point theorems [5].…”

Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg’s model type

“…where M is a closed and convex subset of a Banach space X, see for example [5,8,9,[16][17][18]. Motivated by the observation that the inversion of a perturbed differential operator could yield a sum of a contraction and a compact operator Krasnosel'skii proved in [26] a fixed point theorem, called the Krasnosel'skii's fixed point theorem which appeared as a prototype for solving equations of the previous type.…”