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