New Contributions to Fixed Point Theory for Multi-Valued Feng–Liu Contractions

Abstract

In this paper, we will prove several new results related to the concept of the multi-valued Feng–Liu contraction. An existence, approximation and localization fixed point theorem for a generalized multi-valued nonself Feng–Liu contraction and a new fixed point theorem for multi-valued Feng–Liu contractions in vector-valued metric spaces are proved. Stability results and an application to a system of operatorial inclusions are also given.

Fixed Point Theory for Multi-Valued Feng–Liu–Subrahmanyan Contractions

“…Another open question is to obtain strict fixed point theorems for multi-valued Feng-Liu-Subrahmanyan contractions with closed graph defined on a complete metric space (M, d). For example, we have the following strict fixed point result for multi-valued Feng-Liu-Subrahmanyan contractions, which generalize some theorems in [18,28]. As a matter of fact, the conclusion of the next theorem is Fix(S) = SFix(S) = ∅, which is a quite a usual assumption in various iteration methods for multi-valued operators.…”

“…The following definition was introduced in [18]. Some fixed point results for this class of multi-valued operators are given in the same paper.…”