Fixed Point Theorem and Related Nonlinear Analysis by the Best Approximation Method in p-Vector Spaces. (12th March 2023)

• Record Type: Journal Article
• Authors: Yuan, George Xianzhi
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 4(2023)
• Page Start: 221
• Page End: 295
• Publication Date: 2023-03-12
• Subjects: Best approximation -- condensing mapping -- p-vector space -- locally p-convex space -- fixed point theorem -- graph-approximation -- p-inward and p-outward set -- measure of noncompactness -- nonexpansive mapping -- nonlinear alternative. Leray-Schauder alternative -- nonlinear analysis -- Schauder conjecture -- 1-set contractive mapping -- uniform convex space; 46A16 -- 46A55 -- 52A07 -- 54C60 -- 47H04 -- 47H10 -- 54H25 -- 49J27 -- 49J35 -- 55M20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2023.2167088
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The goal of this paper is to develop some new and useful tools for nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p -convex or p -vector spaces for p ∈ ( 0, 1 ] . In particular, we first develop general fixed point theorems for both set-valued and single-valued condensing mappings which provide answers to the Schauder conjecture in the affirmative way under the setting of (locally p -convex) p -vector spaces, then the best approximation results for upper semi-continuous and 1-set contractive set-valued are established, which are used as tools to establish some new fixed points for non-self set-valued mappings with either inward or outward set conditions under various situations. These results unify or improve corresponding results in the existing literature for nonlinear analysis.