Related papers: Studies on concave Young-functions

In this paper, we study a part of approximation theory that presents the conditions under which a \Ceby\sev set in a Banach space is convex. To do so, we use Gateaux differentiability of the distance function.

The Polyak-{\L}ojasiewicz (P{\L}) inequality extends the favorable optimization properties of strongly convex functions to a broader class of functions. In this paper, we prove a theorem (also obtained by Criscitiello, Rebjock and Boumal in…

This paper's origins are in two papers: One by Colesanti and Fragal\`a studying the surface area measure of a log-concave function, and one by Cordero-Erausquin and Klartag regarding the moment measure of a convex function. These notions…

We propose a fixed-point property for group actions on cones in topological vector spaces. In the special case of equicontinuous actions, we prove that this property always holds; this statement extends the classical Ryll-Nardzewski theorem…

In this paper, we present the Brouwer-Schauder-Tychonoff fixed point theorem on locally convex spaces as the following extension and improvement: Suppose that S is a compact star-shaped subset with respect to p in S with its convexity index…

A scale of the Frechet spaces of exponential type entire functions of one complex variable is considered. Certain special properties of subsets of these spaces consisting of Laguerre entire functions, which are obtained as uniform limits on…

We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift $f(z) \mapsto \frac{f(z)-f(0)}{z}$ is a contraction on the space. We present a model for this operator and…

Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that an affine function with the point of continuity property on X satisfies the minimum principle. As a corollary we obtain a generalization of a…

We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…

We study differentiability properties of functions defined in the euclidean space in terms of a conical square function which is analogue to the classical square function introduced by Stein and Zygmund in the sixties. Pointwise…

Work in the measure algebra of the Lebesgue measure on the Cantor space: for comeager many $[A]$ the set of points $x$ such that the density of $x $ at $A$ is not defined is $\Sigma^{0}_{3}$-complete; for some compact $K$ the set of points…

In this paper, we unify and improve existing results on characterizing strict and almost stricty convex functions via subdifferential mapping, Moreau envelope, and proximal mappings. In particular, it is shown that if a convex function is…

A topological space $X$ has the strong Pytkeev property at a point $x\in X$ if there exists a countable family $\mathcal N$ of subsets of $X$ such that for each neighborhood $O_x\subset X$ and subset $A\subset X$ accumulating at $x$, there…

We introduce the notion of admissible functions and show that the family of L-functions introduced by Lim in [Nonlinear Anal. 46(2001), 113--120] and the family of test functions introduced by Geraghty in [Proc. Amer. Math. Soc., 40(1973),…

Young's convolution inequality provides an upper bound for the convolution of functions in terms of $L^p$ norms. It is known that for certain groups, including Heisenberg groups, the optimal constant in this inequality is equal to that for…

If $f\colon [0,1]^2 \to \mathbb{R}$ is of class $C^2$ then Sard's theorem implies that $f$ has the following relaxed Sard property: the image under $f$ of the Lebesgue measure restricted to the critical set of $f$ is a singular measure. We…

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…

We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckmann maps with singularities. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure $\mu$…

We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the…

For every nonempty compact convex subset $K$ of a normed linear space a (unique) point $c_K \in K$, called the generalized Chebyshev center, is distinguished. It is shown that $c_K$ is a common fixed point for the isometry group of the…