In this paper we consider quasi-concave set functions defined on antimatroids. There are many equivalent axiomatizations of antimatroids, that may be separated into two categories: antimatroids defined as set systems and antimatroids defined as languages. An algorthmic characterization of antimatroids, that considers them as set systems, was given in [4]. This characterization is based on the i...

A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions. 2000 AMS subject classificat...

Polynomials suffice as finite element basis functions for triangles, parallelograms, and some other elements of little practical importance. Rational basis functions extend the range of allowed elements to the much wider class of well-set algebraic elements, where well-set is a convexity type constraint. The extension field from R(x, y) to R(x, y, √ x2 + y2) removes this quadrilateral constrain...

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

Let denote the functions' class that is normalized, analytic, as well univalent in unit disc given by src=image/13426735_01.gif>. Convex, starlike, close-to-convex functions resemble main subclasses of src=image/13426735_02.gif>, expressed src=image/13426735_03.gif>, src=image/13426735_04.gif>, accordingly. Many mathematicians have recently studied radius problem...

This paper’s origins are in two papers: One by Colesanti and Fragalà studying the surface area measure of a log-concave function, one Cordero-Erausquin Klartag regarding moment convex function. These notions same, this paper we continue same construction as well its generalization. In first half prove variation formula for integral functions under minimal optimal conditions. We also explain why...