Results 21 to 30 of about 395 (64)
Monotone Valuations on the Space of Convex Functions
Analysis and Geometry in Metric Spaces, 2015 We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞.
Cavallina L., Colesanti A.
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Open MathematicsIn this article, we establish Hermite-Hadamard-type inequalities for the two classes of functions X±λ(Ω)={f∈C2(Ω):Δf±λf≥0}{X}_{\pm \lambda }\left(\Omega )=\{f\in {C}^{2}\left(\Omega ):\Delta f\pm \lambda f\ge 0\}, where λ>0\lambda \gt 0 and Ω\Omega is ...
Dragomir Silvestru Sever +2 more
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The slope robustly determines convex functions [PDF]
arXiv, 2023 We show that the deviation between the slopes of two convex functions controls the deviation between the functions themselves. This result reveals that the slope -- a one dimensional construct -- robustly determines convex functions, up to a constant of integration.
arxiv
Extension of Fejér's inequality to the class of sub-biharmonic functions
Open MathematicsFejér’s integral inequality is a weighted version of the Hermite-Hadamard inequality that holds for the class of convex functions. To derive his inequality, Fejér [Über die Fourierreihen, II, Math. Naturwiss, Anz. Ungar. Akad. Wiss.
Jleli Mohamed
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Entire Monge-Ampère equations and weighted Minkowski problems [PDF]
arXiv, 2023 In this short note, we prove the existence of solutions to a Monge-Amp\`ere equation of entire type derived by a weighted version of the classical Minkowski problem.
arxiv
A characterization of sets in $\mathbb{R}^2$ with DC distance function [PDF]
arXiv, 2020 We give a complete characterization of closed sets $F \subset \mathbb{R}^2$ whose distance function $d_F:= \mathrm{dist}(\cdot,F)$ is DC (i.e., is the difference of two convex functions on $\mathbb{R}^2$). Using this characterization, a number of properties of such sets is proved.
arxiv
Eventual concavity properties of the heat flow [PDF]
arXiv, 2023 The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for nonnegative, bounded measurable initial functions with compact support.
arxiv
Hermite-Hadamard-type inequalities in the approximate integration [PDF]
Math. Inequal. Appl. 11 (2008), 693-700, 2008 We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.
arxiv +1 more source
Subderivative-subdifferential duality formula [PDF]
arXiv, 2016 We provide a formula linking the radial subderivative to other subderivatives and subdifferentials for arbitrary extended real-valued lower semicontinuous functions.
arxiv
arXiv, 2015 This is a write up on some sections of convex geometry, functional analysis, optimization, and nonstandard models that attract the author.
arxiv