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Abstract: In this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces (in the sense of Kaleva and Seikkala) is discussed. Nonlinear contractions of the Boyd–Wong''s type, Alber–Guerre Delabriere''s type and Kannan–Reich''s type are considered, and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented, respectively. Also, some error estimates are given for iterations to approximate fixed point. Previous work with respect to fixed point in fuzzy metric spaces is based on the t-conorm max. The presented work does away with this restriction, by proposing weaker conditions defining a generic class of suitable binary operations. As applications the corresponding fixed point theorems for Menger probabilistic metric spaces are obtained. [Copyright &y& Elsevier]

Abstract: In the paper “Coupled fixed point theorems for contractions in fuzzy metric spaces” by Sedghi et al. [S. Sedghi, I. Altun, N. Shobec, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72 (2010) 1298–1304], a coupled common fixed point result was presented. However, our purpose is to show that this result and its proof are false. We give a counterexample and also explain how to correct this result. As a modification, we state and prove a coupled fixed point theorem under some hypotheses of fuzzy metric and -norm. [Copyright &y& Elsevier]

Abstract: Several hybrid probabilistic contractions with a gauge function are considered. Using the properties of the pseudo-metric and the triangular norm, some common coupled fixed point theorems are obtained in complete Menger probabilistic metric spaces. The main results are general because they do not assume any continuity or monotonicity conditions for . [Copyright &y& Elsevier]