Note on some recent fixed point theorems in fuzzy metric spaces

Article type: Research Article

Authors: Tanveer, M.

Affiliations: Department of Computer Science & Engineering, The LNM Institute of Information Technology, Jaipur, India

Note: [] Corresponding author. M. Tanveer, Department of Computer Science & Engineering, The LNM Institute of Information Technology, Jaipur, 302 031, India. Tel.: +91 14 1519 1700; Fax: +91 14 1268 9014; E-mails: [email protected]; [email protected]

Abstract: In the recent articles, Khan and Sumitra (Appl. Math. Sci., 5(29)(2011), 1421-1430) and Singh et al. (Int. J. Math. Anal., 5(27) (2011), 1301-1308) claim a fuzzy version of common fixed point theorem of Bouhadjera and Godet-Thobie [3]. The results of aforementioned articles contain flaws and are not correct in their present form. We provide some examples to demonstrate that this claim is false unless some additional conditions are imposed. Our note is desired to complete the interesting results in the quoted paper.

Keywords: Fuzzy metric space, compatible maps, sub compatible maps, sub sequential continuity and reciprocal continuity

DOI: 10.3233/IFS-120772

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 2, pp. 811-814, 2014