Bounded lattice fuzzy coincidence theorems with applications

Article type: Research Article

Authors: Kanwal, Shazia^{a; *} | Azam, Akbar^b

Affiliations: [a] Department of Mathematics, GC University, Faisalabad, Pakistan | [b] Department of Mathematics, COMSATS University, Chak Shehzad, Islamabad, Pakistan

Correspondence: [*] Corresponding author. Shazia Kanwal, Department of Mathematics, GC University, Faisalabad 38000, Pakistan. E-mail: shaziakanwal@gcuf.edu.pk.

Abstract: The main focus of the present paper is to establish a common coincidence point theorem for a pair of L-fuzzy mappings and a non-fuzzy mapping under a generalized φ-contractive condition on a metric space in association with the Hausdorff distance on a class of L-fuzzy sets. A generalized common coincidence point theorem with the dL∞ metric on 1- cuts of L-fuzzy sets is also obtained, which generalizes many recent results in literature. As applications, an analogous coincidence point theorem for crisp mappings is achieved to study some existence theorems of solution for a class of nonlinear integral equations. Even as direct application of coincidence of L- fuzzy mappings, an implicit function theorem is established which can be used to find an explicit restriction of a given implicit relation. For verification and elaboration of our results some interesting and non-trivial examples are presented as well.

Keywords: Coincidence point, implicit function theorem, L-fuzzy mapping, integral equation

DOI: 10.3233/JIFS-181754

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 2, pp. 1531-1545, 2019