Minimization theorem with fuzzy version under quasi-compatible condition (Q1296646)

A nonconvex minimization theorem is established in the context of generating spaces of a quasi-metric family. As application of this result, a fixed point theorem is given for noncommuting maps. The well known results of \textit{J. Caristi} [Trans. Am. Math. Soc. 215, 241-251 (1976; Zbl 0305.47029)] and \textit{D. Downing} and \textit{W. A. Kirk} [Pac. J. Math. 69, 339-346 (1977; Zbl 0357.47036)] are thus generalized. Fuzzy versions of the above theorem are presented in complete fuzzy metric spaces.