Some Inequalities in Quasi 2-normed Space Lp (μ), 0<p<1
Risto Malčeski *
Faculty of Informatics, FON University, Bul. Vojvodina bb, Skopje, Macedonia.
Vesna Manova-Erakovic
Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Skopje, Macedonia.
Aleksa Malčeski
Faculty of Mechanical Engineering, Ss. Cyril and Methodius University, Skopje, Macedonia.
*Author to whom correspondence should be addressed.
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.
Keywords: Quasi 2-norm, (2,p) - norm, modul of concavity