INEQUALITIES OF DUNKL-WILLIAMS AND MERCER IN QUASI 2-NORMED SPACE

Abstract

C. Park [3] introduced the term of quasi 2-normed space, and further he has also proved few properties of quasi 2-norm. M. Kir and M. Acikgoz [4] gave the procedure for completing the quasi 2-normed space. Families of quasi-norms generated by quasi 2-norm are considered in [2] and are also proven few statements according to that ones. The inequalities of Dunkl-Williams, Mercer, Pečarić-Rajić and the sharp parallelepiped inequalities are fundamental in the theory of a 2-normed spaces. In quasi 2-normed spaces are proven, [1] and[2], the analogous inequalities of sharp inequalities and inequalities of Pečarić-Rajić type. In this paper will be considered inequalities, which are analogies to Dunkl-Williams and Mercer inequalities in quasi 2-normed spaces.