Fixed Point Theorems for Upper Semicontinuous Set-valued Mappings in p-Vector Spaces

2022/12/13 by George Xianzhi Yuan, Yuan, George Xianzhi
Computer Science · Mathematics · #46A16 #46A55 #47H04 #47H10 #49J27 #49J35 #52A07 #54C60 #54H25 #55M20 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2303.07177

openalex publication_date 2022/12/13 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mapping in Hausdorff p-vector spaces, and the fixed point theorem for upper semicontinuous set-valued mappings in Hausdorff locally p-convex for p in (0, 1]. These new results provide an answer to Schauder conjecture in the affirmative under the setting of general p-vector spaces for compact single-valued continuous, and also give the fixed point theorems for upper semicontinuous set-valued mappings defined on s-convex subsets in Hausdorff locally p-convex spaces, which would be fundamental for nonlinear functional analysis in mathematics, where s,p in (0.1].

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