Fixed Point Theorems in Generalized Banach Algebras and an Application to Infinite Systems in 𝒞([0, 1], c0) × 𝒞([0, 1], c0). (4th April 2023) - Krichen, Bilel; Mefteh, Bilel; Taktak, Rahma
Abstract: The purpose of this paper is to extend Boyd and Wong's fixed point theorem in complete generalized metric spaces and to apply this result under the so-called G-weak topology in generalized Banach algebras. Some tools will be introduced and involved in our work as the generalized measures of weak non-compactness and the sequential condition ( P G ) . Our results will extend many known theorems in the literature. Also, we will give an application for an infinite system of nonlinear integral equations defined on the generalized Banach algebra ( C ( [ 0, 1 ], c 0 ) × C ( [ 0, 1 ], c 0 ) ), where c 0 is the space of all real sequences converging to zero.