Related papers: Minkowski valuations on convex functions
The Wills functional $\mathcal{W}(K)$ of a convex body $K$, defined as the sum of its intrinsic volumes $\mathrm{V}_i(K)$, turns out to have many interesting applications and properties. In this paper we make profit of the fact that it can…
In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and…
The support measures of a convex body are a common generalization of the curvature measures and the area measures. With respect to the Hausdorff metric on the space of convex bodies, they are weakly continuous. We provide a quantitative…
In Guo and Peng's article [Spherically convex sets and spherically convex functions, J. Convex Anal. 28 (2021), 103--122], one defines the notions of spherical convex sets and functions on "general curved surfaces" in $\mathbb{R}^{n}$…
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
In this paper, we establish some new Ostrowski type inequalities for s-logarithmically convex functions by using Riemann-Liouville fractional integrals. Some applications of our results to P.D.F.'s are given.
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
The classic Riesz representation theorem characterizes all linear and increasing functionals on the space $C_{c}(X)$ of continuous compactly supported functions. A geometric version of this result, which characterizes all linear increasing…
A characterization of Blaschke addition as a map between origin-symmetric convex bodies is established. This results from a new characterization of Minkowski addition as a map between origin-symmetric zonoids, combined with the use of…
New identity for fractional integrals have been defined. By using of this identity, we obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for s-convex, quasi-convex, m-convex functions via Riemann…
The aim of this paper is twofold. On one hand the generalized Minkowski sets are defined and characterized. On the other hand, the Motzkin decomposable sets, along with their epigraphic versions are considered and characterized in new ways.…
A new class of plurisubharmonic functions on the octonionic plane O^2= R^{16} is introduced. An octonionic version of theorems of A.D. Aleksandrov and Chern- Levine-Nirenberg, and Blocki are proved. These results are used to construct new…
In this note we study the Petty projection of a log-concave function, which has been recently introduced in [9]. Moreover, we present some new inequalities involving this new notion, partly complementing and correcting some results from…
We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santal\'o point is at the origin, with those of its inner and outer regularizations. We also provide functional…
We shown that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well…
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
\footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality…
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…