Comments on ‘A common fixed point theorem in a fuzzy metric space’

doi:10.1016/S0165-0114(02)00131-8

Fuzzy Sets and Systems

Volume 135, Issue 3, 1 May 2003, Pages 409-413

https://doi.org/10.1016/S0165-0114(02)00131-8 Get rights and content

Abstract

Our aim in this note is to point out that conditions of some fixed point theorems in a fuzzy metric space recently due to Vasuki are inadequate, and the proof of theorems are false.

References (6)

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There are more references available in the full text version of this article.

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Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073–9] proved some fixed point theorems in intuitionistic fuzzy metric spaces by a strong definition of Cauchy sequence (see [George and Veeramani, Fuzzy Sets Syst 1994;64:395–9] and [Veeramani and Vasuki, Fuzzy Sets Syst 2003;135:409–13]), also the intuitionistic fuzzy metric space has extra conditions (see [Gregori et al., Chaos, Solitons & Fractals, 2006;28:902–5]). In this paper, we consider generalized intuitionistic fuzzy metric spaces i.e., $L$ -fuzzy metric spaces and prove the fuzzy version of Banach and Edelstein contraction theorems in these spaces for modified definition of Cauchy sequence.
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Comments on ‘A common fixed point theorem in a fuzzy metric space’

Abstract

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Inform. Control