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We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma…
We introduce a new operation between nonnegative integrable functions on $\mathbb{R} ^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature…
Some new Hermite-Hadamard's inequalities for h-convex functions are proved, generalizing and unifying a number of known results. Some new applications for special Means of real numbers are also derived.
L$^\natural$ (natural)-convex functions encompass a large class of nonlinear functions over general integer domains and arise in a wide range of real-world applications. We explore the minimization of L$^\natural$-convex functions, of…
We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath\'eodory--Fej\'er--Tur\'an problem. The first variation imposes the additional requirement that the function is…
We study a sharp fractional Moser-Trudinger type inequality in dimension 1, its compactness properties and the critical points of a functional associeted to the inequality.
We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series.…
An inequality of Brascamp-Lieb-Luttinger and of Rogers states that among subsets of Euclidean space $\mathbb{R}^d$ of specified Lebesgue measures, balls centered at the origin are maximizers of certain functionals defined by…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We consider second-order elliptic equations in non-divergence form with oblique derivative boundary conditions. We show that any strong solutions to such problems are twice continuously differentiable up to the boundary provided that the…
We introduce $ L $-functions attached to negative definite plumbed manifolds as the Mellin transforms of homological blocks. We prove that they are entire functions and their values at $ s=0 $ are equal to the Witten--Reshetikhin--Turaev…
We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…
We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and…
Our aim in this paper, is to establish certain new integrals for the the (p,q)-Mathieu--power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of thus special function. Moreover, we…
An inequality of Brascamp-Lieb-Luttinger generalizes the Riesz-Sobolev inequality, stating that certain multilinear functionals, acting on nonnegative functions of one real variable with prescribed distribution functions, are maximized when…
For continuous functions, midpoint convexity characterizes convex functions. By considering discrete versions of midpoint convexity, several types of discrete convexities of functions, including integral convexity, L$^\natural$-convexity…
Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the…
Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…
The introduction of a fractional differential operator defined in terms of the Riemann-Liouville derivative makes it possible to generalize the kinetic equations used to model relaxation in dielectrics. In this context such fractional…