Related papers: Notes on the functional LYZ ellipsoid

The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well. The operator…

Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable…

For a given function from a set to itself, we can define a directed graph called the functional graph, where the vertices are the elements of the set, and the edges are all the pairs of inputs and outputs for the function. In this article…

We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.

In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…

We consider functional ellipsoids in the sense defined by Ivanov and Nasz\'odi and we study the problem of constructing a decomposition of the identity similar to the one given by Fritz John in his fundamental theorem.

A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin…

$L$-functions can be viewed axiomatically, such as in the formulation due to Selberg, or they can be seen as arising from cuspidal automorphic representations of $\textrm{GL}(n)$, as first described by Langlands. Conjecturally these two…

We give a functional equation for the refined Herglotz-Zagier function. It is analogous to a result in the theory of modular forms.

We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials

We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.

We extend the notion of Ulam floating sets from convex bodies to Ulam floating functions. We use the Ulam floating functions to derive a new variational formula for the affine surface area of log-concave functions.

We give two different definitions of what it means for a matrix-valued function to be log concave, guided by similar notions in complex differential geometry. After discussing a few simple examples, we proceed to develop some of the basic…

The well-known Jacobi elliptic functions sn(z)$, $cn(z), dn(z) are defined in higher dimensional spaces by the following method. Consider the Clifford algebra of the antieuclidean vector space of dimension 2m+1. Let x be the identity…

We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.

In the present paper two certain subclasses of the starlike functions associated with the vertical strip are considered. The main aim of this paper is to investigate some basic properties of these classes such as, subordination relations,…

We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…

We develop an elementary formalism of functional calculus for entire holomorphic functions in the setting of Clausen and Scholze's $p$-liquid vector spaces.

By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…

In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…