Abstract: The concept of a generalized local power contractive mapping is introduced in generating spaces of quasi-metric family.The boundedness of mapping orbit and the convergence of iterative sequence are discussed.By means of these properties,some fixed point theorems for generalized local power contractive mapping are established in generating spaces of quasi-metric family.These results not only unify and extend the corresponding results of usual metric spaces and Menger probabilistic metric spaces,but also contain the fixed point theorems for contraction type mappings in Kaleva-Seikkala fuzzy metric spaces as their special cases.

Key words: quasi-metric family, generalized local power contractive mapping, orbit, iterative sequence, fixed point, fuzzy metric space, probabilistic metric space