Measures of weak noncompactness and fixed point theory in Banach algebras satisfying condition (<i>P</i>)

Abstract

Abstract. The aim of this paper is to prove some new fixed point theorems in a nonempty closed convex subset of a Banach algebra satisfying a sequential condition (P) in a weak topology setting.

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.…”

“…where Ω is a nonempty, bounded, closed, and convex subset of a Banach algebra X and B is a compact operator from Ω into X. Many authors [10,11,13,14] generalized Equation (1) to the equation:…”