Graph contractions in vector-valued metric spaces and applications. (3rd April 2021)

• Record Type: Journal Article
• Authors: Petruşel, Adrian; Petruşel, Gabriela; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 763
• Page End: 775
• Publication Date: 2021-04-03
• Subjects: Non-self graph (orbital) contraction -- vector-valued metric -- fixed point -- stability properties -- coincidence problem; 47H10 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1713130
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we will present a study of the fixed point equation x = f ( x ), x ∈ X (where ( X, d ) is a generalized metric space in the sense that d ( x, y ) ∈ R + m and f : X → X is a graph contraction) by the following perspectives: existence, uniqueness, approximation, data dependence of the operator perturbation, well-posedness, and Ulam-Hyers stability. The non-self case is also discussed and some applications are given.