Fixed Point Theorems for Weakly Asymptotically Regular Mappings in Banach Spaces with an Application. (2nd January 2022)

• Record Type: Journal Article
• Authors: Jeribi, Aref; Kaddachi, Najib; Laouar, Zahra
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 1(2022)
• Page Start: 68
• Page End: 87
• Publication Date: 2022-01-02
• Subjects: De Blasi measure of weak noncompactness -- fixed point theorems -- non-separable Banach space -- weakly semi-closed at the origin -- weakly sequentially continuous; 47H08 -- 47H10 -- 58C30 -- 19K56; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2001820
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Using the technique of measures of weak non-compactness we obtain the existence of fixed points of a 2 × 2 block operator matrix involving nonlinear maps in non-separable Banach space. These theorems are created in terms of weak sequential continuity and the theory of countably condensing maps. Our results generalize, improve and complement a number of earlier works. The obtained results are then applied to a coupled system of nonlinear functional integral equations.