Some critical remarks on recent results concerning ϝ−contractions in b-metric spaces

• Published in: Cubo (Temuco, Chile) Vol. 25; no. 1; pp. 57 - 66
• Main Authors: Younis, Mudasir, Mirkov, Nikola, Savić, Ana, Pantović, Mirjana, Radenović, Stojan
• Format: Journal Article
• Language: English; Portuguese
• Published: Universidad de La Frontera. Departamento de Matemática y Estadística 01.04.2023; Universidad de La Frontera
• Subjects: b-metric space; b–common fixed point; MATHEMATICS; MATHEMATICS, APPLIED; v_s–complete; ϝ-contraction; υ s−complete; ϝ−contraction, b−common fixed point; b−metric space
• ISSN: 0719-0646; 0716-7776; 0719-0646
• DOI: 10.56754/0719-0646.2501.057

Abstract This paper aims to correct recent results on a generalized class of ϝ −contractions in the context of b−metric spaces. The significant work consists of repairing some novel results involving ϝ −contraction within the structure of b-metric spaces. Our objective is to take advantage of the property (F1) instead of the four properties viz. (F1), (F2), (F3) and (F4) applied in the results of Nazam et al. [“Coincidence and common fixed point theorems for four mappings satisfying (αs, F)−contraction", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664-690, 2018]. Our approach of proving the results utilizing only the condition (F1) enriches, improves, and condenses the proofs of a multitude of results in the existing state-of-art.