Generalized distance and existence theorems in complete metric spaces

In this paper. we first introduce the concept of tau -distance on a metric space, which is a generalized concept of both w-distance and Tataru's distance. We also improve the generalizations of the Banach contraction principle, Caristi's fixed point theorem, Ekeland's variational principle, and the nonconvex minimization theorem according to Takahashi. Further we discuss the relation between w-distance and Tataru's distance, (C) 2001 Academic Press.