Fixed points for α − βe-geraghty contractions on b-metric spaces and applications to matrix equations

Abstract

In this paper, we introduce the notion of α − βE-Geraghty contraction type mappings on b-metric spaces and prove the existence and uniqueness of fixed point for such mappings. These results are generalizations of the recent results in [Fulga and Proca, Fixed points for ϕE-Geraghty contractions, J. Nonlinear Sci. Appl. 10 (2017), 5125-5131]. We give some examples illustrating the presented results. An application on matrix equations and numerical algorithms are also provided.