Fixed point theorems for L-fuzzy mappings in L-fuzzy metric spaces

Article type: Research Article

Authors: Imdad, Mohammad^a | Ahmed, Mohammed A.^b | Nafadi, Hatem A.^c | Sharma, Anupam^{d; *}

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [b] Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt | [c] Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt | [d] Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

Correspondence: [*] Corresponding author. Anupam Sharma, Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India. E-mail: [email protected].

Abstract: In this paper, we prove fixed points for hybrid pairs of L -fuzzy and non-self mappings in non-Archimedean L -fuzzy metric spaces. First, we define the notion of joint common limit range property ((JCLR) property) in such spaces. Further, we prove some common fixed point theorems for L -fuzzy and non-self mappings in non-Archimedean L -fuzzy metric spaces. Also, an integral contractive condition and implicit relation have been used in some results. These theorems extend, generalize and improve corresponding previous results in metric, fuzzy metric and L -fuzzy metric spaces.

Keywords: ℒ–Fuzzy metric spaces, ℒ–fuzzy mappings, (JCLR) property, common fixed point

DOI: 10.3233/JIFS-171033

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 1, pp. 683-692, 2018