Related papers: Complete Monotonicity and Inequalities of Function…
We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency.
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…
In this note our aim is to deduce some new monotonicity properties for a special combination of Bessel functions of the first kind by using a recently developed Mittag-Leffler expansion for the derivative of a normalized Bessel function of…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties of holomorphic motions over almost…
The purpose of this paper is to study various monotonicity conditions of the period function $T(c)$ (energy-dependent) for potential systems $\ddot x + g(x)=0$ with a center at the origin 0. We had before identified a family of new criteria…
Let $\psi(x)$ be the di-gamma function, the logarithmic derivative of the classical Euler's gamma function $\Gamma(x)$. In the paper, the author shows that the completely monotonic degree of the function $[\psi'(x)]^2+\psi''(x)$ is $4$,…
In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution…
An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities…
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show that many properties which $\Ga(z)$ enjoys extend in a…
In this paper we prove monotonicity of some ratios of $q$--Kummer confluent hypergeometric and $q$--hypergeometric functions. The results are also closely connected with Tur\'an type inequalities. In order to obtain main results we apply…
The results on $\Gamma$-limits of sequences of free-discontinuity functionals with bounded cohesive surface terms are extended to the case of vector-valued functions. In this framework, we prove an integral representation result for the…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
In this paper, we present and prove some generalizations of some inequalities for the $p$-Gamma, $q$-Gamma and $k$-Gamma functions. Our approach makes use of the series representations of the psi, $p$-psi, $q$-psi and $k$-psi functions.
It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine properties of the classical gamma function.