Some Orlicz-Brunn-Minkowski type inequalities for (dual) quermassintegrals of polar bodies and star dual have been introduced. In this paper, we generalize the results establish some mixed bodies.

In this paper, the author examines Holder’s inequality and related inequalities in probability. The paper establishes new inequalities in probability that generalize previous research in this area. The author places Beckenbach’s (1950) inequality in probability, from which inequalities are deduced that are similar to Brown’s (2006) inequality along with Olkin and Shepp (2006). For convenience, ...

The classical Brunn-Minkowski theory for convex bodies was developed from a few basic concepts: support functions, Minkowski combinations, and mixed volumes. As a special case of mixed volumes, the Quermassintegrals are important geometrical quantities of a convex body, and surface area measures are local versions of Quermassintegrals. The Christoffel-Minkowski problem concerns with the existen...

minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. also related inequalities to minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. several examples are given to illustrate the validity of theorems. some results on chebyshev and minkowski type inequalities are obtained.

The aim of this paper is to motivate the development of a Brunn-Minkowski theory for minimal surfaces. In 1988, H. Rosenberg and E. Toubiana studied a sum operation for finite total curvature complete minimal surfaces in R3 and noticed that minimal hedgehogs of R3 constitute a real vector space [14]. In 1996, the author noticed that the square root of the area of minimal hedgehogs of R3 that ar...

Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in R. They are the natural geometrical objects when one seeks to extend parts of the Brunn-Minkowski theory to a vector space which contains convex bodies. In terms of characteristic functions, Minkowski addition of convex bodies correspond to convolution with respect to th...

In 1990, E. Baum gave an elegant polynomial-time algorithm for learning the intersection of two origin-centered halfspaces with respect to any symmetric distribution (i.e., any D such that D(E) = D(−E)) [3]. Here we prove that his algorithm also succeeds with respect to any mean zero distribution D with a log-concave density (a broad class of distributions that need not be symmetric). As far as...