Abstract
Special properties that the scalar product enjoys and its close link with the norm function have raised the interest of researchers from a very long period of time. S.S. Dragomir presents concrete generalizations of the scalar product functions in a normed space and deals with the interesting properties of them. Based on S.S. Dragomirs idea in this paper we treat generalizations of superior and inferior scalar product functions in the case of semi-normed spaces and 2-normed spaces.
Highlights
Definition 1.1 Let X be a complex (real) vector space
Before explaining the main results of this paper, we introduce some common known concepts.Definition 1.1 Let X be a complex vector space
Definition 1.2: A semi norm is a function on vector space X, denoted p(x) such that the following conditions hold: 1. p(x) 0
Summary
Definition 1.1 Let X be a complex (real) vector space. We shall say that a complex (real) semi inner product is defined on X , if to any x, y X there corresponds a complex (real) number (x, y) and the following properties hold: 1. We call X a complex (real) semi inner product space. Definition 1.2: A semi norm is a function on vector space X , denoted p(x) such that the following conditions hold: 1.
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