Some Inequalities in Quasi 2-normed Space Lp (μ), 0

Abstract

In [1], C. Park generalized the notion of the quasi-normed space, i.e. he introduced the notion of the quasi 2-normed space. He proved several properties of the quasi 2-norm. In [2], M. Kir and M. Acikgoz gave the procedure of completing the quasi 2-normed space. Several inequalities relating the quasi 2-normed spaces are given in [3,4,5]. Later, in [6], some properties of the convergent sequences in quasi 2-normed spaces are proven. In this paper, we will introduce the quasi 2-norm of the space Lp (μ), 0<p<1 and we will prove several inequalities relating the quasi 2-norm of this space.