35 research outputs found
Angular equivalence of normed spaces
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of norm equivalence. Angularly equivalent norms share certain geometric properties: A norm that is angularly equivalent to a uniformly convex norm is itself uniformly convex. The same is true for strict convexity. Extreme points of the unit balls of angularly equivalent norms occur on the same rays, and if one unit ball is a polyhedron so is the other. Among norms arising from inner products, two norms are angularly equivalent if and only if they are topological equivalent. But, unlike topological equivalence, angular equivalence is able to distinguish between different norms on a finite-dimensional space. In particular, no two norms on are angularly equivalent.http://www.elsevier.com/locate/jmaa2018-10-15hj2017Mathematics and Applied Mathematic
Three geometric constants for Morrey spaces
In this paper we calculate three geometric constants, namely the von
Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant,
for Morrey spaces and discrete Morrey spaces. These constants measure uniformly
nonsquareness of the associated spaces. We obtain that the three constants are
the same as those for and spaces
JensenâOstrowski inequalities and integration schemes via the Darboux expansion
By using the Darboux formula obtained as a generalization of the Taylor formula, we deduce some JensenâOstrowski-type inequalities. The applications to quadrature rules and f-divergence measures (specifically, for higher-order Ď-divergence) are also presented.http://link.springer.com/journal/11253hj2019Mathematics and Applied Mathematic