Related papers: Completely monotone functions - a digest
Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $\mu$, i.e., $\mathrm{d}\mu(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus…
A metric space (X,d) is monotone if there is a linear order < on X and a constant c>0 such that d(x,y) < c d(x,z) for all x<y<z in X. Properties of continuous functions with monotone graph (considered as a planar set) are investigated. It…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
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…
This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on bounded convex sets, a complete characterization of this…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
Some real functions f induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define linear mapping beta on matrices (which is basic in the…
Motivated by several conjectures posed in the paper " Completely monotonic degrees for a difference between the logarithmic and psi functions",we confirm in this work some conjectures on completely monotonic degrees of remainders of the…
Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical…
We study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We also investigate under…
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral…
We study operator log-convex functions on $(0,\infty)$, and prove that a continuous nonnegative function on $(0,\infty)$ is operator log-convex if and only if it is operator monotone decreasing. Several equivalent conditions related to…
The elliptic integral and its various generalizations are playing very important and basic role in different branches of modern mathematics. It is well known that they cannot be represented by the elementary transcendental functions.…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
The main focus of this paper is to study multi-valued linear monotone operators in the contexts of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness,…
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…