ASYMMETRIC INNER PRODUCT AND THE ASYMMETRIC QUASI NORM FUNCTION

Abstract

This paper attempts to generalize the semi scalar product concept according to G. Lumer by replacing Cauchy inequality with another inequality which is more generalized. Based on this attempt of generalization it is built a function which fulfils the conditions which are changed. In this paper it is also generalized quasi norm function by replacing homogeneity condition with a more restricted condition by producing this time a more generalized asymmetric semi norm function. As a result, in this paper it is defined the asymmetric inner product function and the asymmetric quasi norm function. Moreover, it is even given relation between these two.