On generalization of an semi-inner product function

Abstract

The concept of inner product lays an important role in functional analysis and in its applications. Starting from its axiomatic, many researches have made various modifications passing in its generalization, such as semi-inner product. In fact, in this paper we define an semi-inner product function by modifying linearity concerning two variables of inner product, gaing a norm function and consequently a locally convex vectorial space.