George Xianzhi Yuan, Wei-Shih Du, New nonlinear principles and fixed point theorems in locally p-convex spaces, Vol. 2027 (2027), No. 5, pp. 1-24

Full Text: PDF
DOI: 10.23952/cot.2027.5

Received August 18, 2025; Accepted March 15, 2026; Published online July 13, 2026

Abstract. The goal of this paper is to establish fixed point theorems for non-self F contraction and non-self nonexpansive set-valued mappings by applying Caristi fixed point theorem as a tool in locally p-convex spaces, where $p \in (0, 1]$ . In particular, we first derive a few of key principles widely used in nonlinear analysis and optimization by using Caristi fixed point theorem as a tool in both complete metric spaces and locally complete p-convex spaces, where $p \in (0, 1]$ , respectively. Secondly, as applications of Caristi fixed point theorem being a starting point, we establish fixed point theorems for non-self F contraction and non-self nonexpansive set-valued mappings in locally complete p-convex spaces. These results improve or unify corresponding results in the literature.

How to Cite this Article:
G.X. Yuan, W.S. Du, New nonlinear principles and fixed point theorems in locally p-convex spaces, Commun. Optim. Theory 2027 (2027) 5.