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)

• Record Type: Journal Article
• Authors: Krichen, Bilel; Mefteh, Bilel; Taktak, Rahma
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 5(2023)
• Page Start: 333
• Page End: 367
• Publication Date: 2023-04-04
• Subjects: ϕ-contractive mappings -- condition (PG) -- generalized Banach space -- generalized measures of weak non-compactness -- integral equations system; 47H10 -- 45G15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2023.2172033
• Languages: English
• ISSNs: 0163-0563

Abstract

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.