Fixed Point Theory for Multi-valued Feng–Liu Operators in Vector-Valued Metric Spaces

The most important metric fixed point theorem for multi-valued operators is the Multi-valued Contraction Principle proved by S. B. Nadler Jr. in 1969. One of the most relevant generalizations of it was proposed by Y. Feng and S. Liu in 2006. In this work, which is a synthesis of some previous papers of the authors, we will present an extension of the fixed point result of Feng and Liu for the case of a set X endowed with a vector-valued metric in the sense of Perov. Existence, localization, data dependence and different kinds of stability properties of a fixed point inclusion with a generalized multi-valued Feng–Liu operator are presented. An extension to the so-called multi-valued contractions of the Feng–Liu–Subrahmanyan type is also considered. Some applications are suggested.