Fixed Point Theorems for Upper Semicontinuous Set-valued Mappings in $p$-Vector Spaces
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].
Cite
@article{arxiv.2303.07177,
title = {Fixed Point Theorems for Upper Semicontinuous Set-valued Mappings in $p$-Vector Spaces},
author = {George Xianzhi Yuan},
journal= {arXiv preprint arXiv:2303.07177},
year = {2023}
}
Comments
13 pages; no figures. arXiv admin note: substantial text overlap with arXiv:2210.10286