On Caristi fixed point theorem for set-valued mappings - Chaira, Karim; Chaira, Soumia; Lazaiz, Samih (Topological Methods in Nonlinear Analysis, 2022)
The aim of this paper is to discuss Penot's problem on a generalization of Caristi's fixed point theorem.We settle this problem in the negative and we present some new theorems on the existence of fixed points of set-valued mappings inordered metric spaces and reflexive Banach spaces.