Fixed point theorems for nonlinear contractions in Kaleva–Seikkala's type fuzzy metric spaces

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.