A generalized fixed-point theorem for set-valued mappings in b-metric spaces

Abstract

The aim of this article is to present a local generalized fixed-point theorem for set-valued mappings in b-metric spaces, which brings together the framework of different (such as Nadler’s and Kannan’s) fixed-point theorems. For general set-valued graph contractions, a global fixed-point theorem and qualitative results concerning the fixed-point sets are obtained. We also provide an answer to the open question regarding Ulam-Hyers stability of the fixed-point inclusion proposed in [Petruşel et al., Multi-valued graph contraction principle with applications, Optimization 69 (2020), 1541–1556].

Keywords

• fixed-point
• general graph contraction
• ulam-hyers stability
• b-metric space
• 47h10
• 49j53
• 54h25