2k-inner products and 2k-Riemannian metrics

Abstract

The notion of 2k-inner product is introduced as a generalization of usual inner product and Q-inner product([4]-[8]). As a consequence, is defined the notion of 2k-normed space and some properties, e.g. uniformly convexity, Gâteaux differentiability and Riesz propriety of the dual, are given. Also, the notion of 2k-Riemannian metric is introduced