Convessità in dimensione finita
Convex and monotone operator functions
The purpose of this note is to provide characterizations of operator convexity and give an alternative proof of a two-dimensional analogue of a theorem of Löwner concerning operator monotonicity.
Convex differentiable set-valued functions.
Convex functions and inequalities for integrals.
Convex functions and the Hadamard inequality.
Convex functions of higher orders in Euclidean spaces
Convex functions with respect to logarithmic mean and ѕandwich theorem
Convex sets and inequalities.
Convex transformations with Banach lattice range.
A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching...
Convexity and almost convexity in groups
We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...
Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means.
Convexity of weighted Stolarsky means.
Convexity properties and inequalities for a generalized gamma function.
Convexity with given infinite weight sequences.
Convexity-like inequalities for averages in a convex set.
Convexity-like inequalities for averages in a convex set. (Summary).
Convex-like inequality, homogeneity, subadditivity, and a characterization of -norm
Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the -norm.
Convolution inequalities and applications.
Convolution of radius functions on ℝ³
We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in the boundary...
Convolution operators with homogeneous singular measures on of polynomial type. The remainder case.