AROUND PEROV'S FIXED POINT THEOREM FOR MAPPINGS ON GENERALIZED METRIC SPACES.

We revisit Perov's fixed point theorem for selfmaps of a set endowed with a vector metric taking values in the Euclidean space Rm. In particular, we show that this result is subsumed by the classical Banach contraction principle. We also obtain a generalization of Perov's theorem by con- sidering mappings on K-metric spaces satisfying a nonlinear Lipschitz condition. Two applications are presented and some characterizations of convergence in K-metric spaces are given. [ABSTRACT FROM AUTHOR]