New fixed point theorems for set-valued contractions in b-metric spaces

TL;DR

This paper extends fixed point theorems for set-valued contractions within b-metric spaces, generalizing classical results like Nadler's contraction principle and a theorem by Aydi et al., broadening their applicability.

Contribution

It introduces a generalized framework for fixed point theorems in b-metric spaces, extending key results for set-valued contractions and quasi-contractions.

Findings

Extended Nadler's contraction principle to b-metric spaces

Generalized fixed point theorem for set-valued quasi-contractions

Provided examples illustrating the new theorems

Abstract

In this paper we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler's contraction principle for set-valued functions (see Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475-488) and a fixed point theorem for set-valued quasi-contractions functions due to H. Aydi, M.F. Bota, E. Karapinar and S. Mitrovic (see A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012:88).