Related papers: Complete monotonicity of a function involving the …

In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.

Let $F_{p}(x) =L( t^{p}f(t)) =\int_{0}^{\infty }t^{p}f(t) e^{-xt}dt$ converge on $(0,\infty)$ for $p\in \mathbb{N}_{0}=\mathbb{N}\cup{0}$, where $f(t)$ is positive on $(0,\infty)$. In a recent paper [Z.-H. Yang, A complete monotonicity…

In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…

The function $G(x)=(1-\ln x /\ln(1+x))x\ln x$ has been considered by Alzer, Qi and Guo. We prove that $G'$ is completely monotonic by finding an integral representation of the holomorphic extension of $G$ to the cut plane. A main difficulty…

We discuss the problem of classifying polynomials $p : \mathbb R^2_+ \rightarrow (0, \infty)$ for which $\frac{1}{p}=\{\frac{1}{p(m, n)}\}_{m, n \geq 0}$ is joint completely monotone, where $p$ is a linear polynomial in $y.$ We show that if…

Let $\mathcal{L}(x,a)$ be defined on $\left( -1,\infty \right) \times \left( 4/15,\infty \right) $ or $\left( 0,\infty \right) \times \left( 1/15,\infty \right) $ by the formula% \begin{equation*} \mathcal{L}(x,a)=\tfrac{1}{90a^{2}+2}\ln…

In this work we prove that if an entire function $f(z)$ is of order strictly less than one and it has only negative zeros, then for each nonnegative integer $k,m$ the real function…

We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…

We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the…

In this paper, the algebra of the differences of two multiply monotone functions on $\mathbb{R}_+=(0,+\infty)$ is studied. A sufficient condition for the function $f_0\big(|x|_{p,d}\big)$, where…

We prove that the function $g(x)= 1 / \bigl( 1 - \cos(x) \bigr)$ is completely monotonic on $(0,\pi]$ and absolutely monotonic on $[\pi, 2\pi)$, and we determine the best possible bounds $\lambda_n$ and $\mu_n$ such that the inequalities $$…

This paper systematically investigates the absolute monotonicity of two function families associated with the Gaussian hypergeometric function $F(a, b; c; x)$ (where $a,b,c\in\mathbb{R}_+$): $\mathcal{F}_p(x)=(1-x)^pF(a,b;c;x)$ and…

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential…

In the paper, the authors verify the complete monotonicity of the difference $e^{1/t}-\psi'(t)$ on $(0,\infty)$, compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion…

To verify the universal validity of the "two-sided" monotonicity condition introduced in [8], we will apply it to include more classical examples. The present paper selects the $L^{p}$ convergence case for this purpose. Furthermore, Theorem…

In this article we first establish the maximum principle of the antisymmetric functions for parabolic fractional $p$-equations. Then we use it and the parabolic inequalities to provide a different proof of symmetry and monotonicity for…

We consider the following question: if a function of the form $\int_0^{\infty}\varphi(t)\, e^{-xt}dt$ is completely monotonic, is it then $\varphi\ge0$? It turns out that the question is related to a moment problem. In the end we apply…

We introduce the notion of Dunkl completely monotonic functions on $\left(-\sigma,\sigma\right), \sigma>0$. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.

It is shown that a function $f$ is a generalized Stieltjes function of order $\lambda>0$ if and only if $x^{1-\lambda}(x^{\lambda-1+k}f(x))^{(k)}$ is completely monotonic for all $k\geq 0$, thereby complementing a result due to Sokal.…