Contractions in fuzzy rectangular b-metric spaces with application

Article type: Research Article

Authors: Mehmood, Faisar^a | Ali, Rashid^{a; *} | Hussain, Nawab^b

Affiliations: [a] Capital University of Science and Technology, Islamabad, Pakistan | [b] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Correspondence: [*] Corresponding author. Rashid Ali, Capital University of Science and Technology, Islamabad, Pakistan. E-mail: [email protected].

Abstract:  In this paper, by introducing the concept of a fuzzy rectangular-b-metric space, the notion of a fuzzy metric space and a fuzzy b-metric space are generalized. The well known metric fixed point theorems are established in the setting of fuzzy rectangular b-metric spaces and illustrated by examples. To show the significance of our result an application is presented to establish the existence of a solution of integral equation. Our results generalize many existing theorems in the literature.

Keywords: b-metric space, Fuzzy b-metric space, Fixed points, Contractions

DOI: 10.3233/JIFS-182719

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1275-1285, 2019