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.

Keywords

• multi-valued operator
• fixed point
• strict fixed point
• vector-valued metric
• local fixed point theorem
• stability properties