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- Title
FIXED POINT THEOREMS FOR CONTINUOUS SINGLE-VALUED AND UPPER SEMICONTINUOUS SET-VALUED MAPPINGS IN <sub>p-</sub>VECTOR AND LOCALLY <sub>p-</sub>CONVEX SPACES.
- Authors
YUAN, GEORGE X.
- Abstract
The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mappings in Hausdorff p-vector spaces, and a fixed point theorem for upper semicontinuous set-valued mappings in locally p-convex spaces for p 2 (0; 1]. These results not only provide a solution to Schauder conjecture in the affirmative under the setting of p-vector spaces for compact single-valued continuous mappings, but also show the existence of fixed points 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, where s; p 2 (0; 1].
- Subjects
SET-valued maps; NONLINEAR functional analysis; FIXED point theory; FUNCTIONAL analysis; HAUSDORFF spaces; COMPACT spaces (Topology)
- Publication
Topological Methods in Nonlinear Analysis, 2024, Vol 63, Issue 1, p209
- ISSN
1230-3429
- Publication type
Article
- DOI
10.12775/TMNA.2023.027