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Abstract  

Using the theory of countable extension of t-norm we prove a common fixed point theorem for compatible mappings satisfying an implicit relation in fuzzy metric spaces.

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Abstract  

In the recent paper of this journal [7], a common fixed point theorem in G-complete fuzzy metric spaces under the t-norm Min was proved. We show that this theorem actually holds in more general situations.

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Abstract  

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc.

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Abstract  

In the recent paper [1] the claim is made that a probabilistic version of a common fixed point theorem of Pant holds. 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.

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Abstract  

V. Gregori and S. Romaguera [17] obtained an example of a fuzzy metric space (in the sense of A. George and P. Veeramani) that is not completable, i.e. it is not isometric to a dense subspace of any complete fuzzy metric space; therefore, and contrary to the classical case, there exist quiet fuzzy quasi-metric spaces that are not bicompletable neither D-completable, via (quasi-)isometries. In this paper we show that, nevertheless, it is possible to obtain solutions to the problem of completion of fuzzy quasi-metric spaces by using quasi-uniform isomorphisms instead of (quasi-)isometries. Such solutions are deduced from a general method, given here, to obtain extension properties of fuzzy quasi-metric spaces from the corresponding ones of the classical theory of quasi-uniform and quasi-metric spaces.

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] Mihet , D. 2010 Fixed point theorems in fuzzy metric spaces using property E.A Nonlinear Anal. 73 2184 – 2188 10.1016/j.na.2010

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