A novel framework of complex valued fuzzy metric spaces and fixed point theorems¹

Article type: Research Article

Authors: Singh, Deepak^a | Joshi, Vishal^b | Imdad, Mohammad^c | Kumam, Poom^{d; e; *}

Affiliations: [a] Department of Applied Sciences, NITTTR, Under Ministry of HRD, Govt. of India, Bhopal, (M.P.), India | [b] Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur, (M.P.), India | [c] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [d] Theoretical and Computational Science Center (TaCS) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok, Thailand | [e] China Medical University, Taichung, Taiwan

Correspondence: [*] Corresponding author. Poom Kumam. Tel.: +66 0 2470 8994; Fax: +66 0 2428 4029; E-mails: poom.kum@kmutt.ac.th and poom.kumam@mail.kmutt.ac.th.

Note: [1] This research was supported by the Theoretical and Computational Science Center (TaCS-Center) (Grant No. TaCS2558-1).

Abstract: In this article, recognizing the innovative concept of complex valued fuzzy set due to Ramot et al. [1], we introduce the notion of complex valued fuzzy metric spaces. Several allied topological aspects for complex valued fuzzy metric spaces are also defined which fortify the concept. Moreover the complex valued fuzzy version of some celebrated and essential results from metric spaces including Banach contraction principle and the main theorem of Jungck [2] are established. Additionally some fixed point theorems satisfying certain rational expressions are proved.

Keywords: Complex fuzzy set, complex valued fuzzy metric spaces, cauchy sequence, complex valued complete fuzzy metric, fixed point theorem, rational expression

DOI: 10.3233/IFS-152065

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3227-3238, 2016