相关论文: Logarithmically complete monotonicity of reciproca…
This note contains some observations on primary matrix functions and different notions of monotonicity with relevance towards constitutive relations in nonlinear elasticity. Focussing on primary matrix functions on the set of symmetric…
In this short note we prove that, if (C[a,b],{A_n}) is an approximation scheme and (A_n) satisfies de La Vall\'ee-Poussin Theorem, there are instances of continuous functions on [a,b], real analytic on (a,b], which are poorly approximable…
Using the ideas of Deninger, we prove that the Artin $L$-functions coincide with such of the noncommutative tori. This result can be viewed as the Langlands reciprocity for noncommutative tori.
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…
Euler's gamma function is logarithmically convex on positive semi-axis. Additivity of logarithmic convexity implies that the function sum of gammas with non-negative coefficients is also log-convex. In this paper we investigate the series…
The Ramanujan sequence $ \{\theta_{n}\}_{n \geq 0}$, defined as $$ \theta_{0}= \frac{1}{2} \ , \ \ \ \theta_{n} = \left(\ \ \frac{e^{n}}{2} - \sum_{k=0}^{n-1} \frac{n^{k}}{k !} \ \ \right) \cdot \frac{n !}{n^{n}} \ , \ \ n \geq 1 \ ,$$ has…
The monotonicity properties of remainder of Stirling's formula for the gamma function are simply obtained by using the integral transforms with series.
Let $0<p\leq 1$, and let $\omega:\mathbb N^2 \to [1,\infty)$ be an almost monotone weight. Let $\mathbb H$ be the closed right half plane in the complex plane. Let $\widetilde a$ be a complex valued function on $\mathbb H^2$ such that…
Complete monotonicity, Laguerre and Tur\'an type inequalities are established for the so-called Kr\"atzel function $Z_{\rho}^{\nu},$ defined by $$Z_{\rho}^{\nu}(u)=\int_0^{\infty}t^{\nu-1}e^{-t^{\rho}-\frac{u}{t}}\dt,$$ where $u>0$ and…
We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is no equivalence between the absolute continuity of a function…
We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first…
In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q-functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two…
In the paper, the author presents a double inequality for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic…
The comonotonic maxitivity property of functionals frequently appears in the characterization of fuzzy integrals based on the maximum operation. In some special cases, comonotonic maxitivity implies monotonicity of functionals. The question…
In this present investigation, we found a set of sufficient conditions to be imposed on the parameters of the Fox H-functions which allow us to conclude that it is non-negative. As applications, various new facts regarding the Fox-Wright…
For $a\in(0,1)$, $r\in(0,1)$ and $K\in(1,\infty)$, let $\mu_{a}(r)$ and $\varphi_{K}^{a}(r)$ be the generalized Gr\"{o}tzsch ring function and generalized Hersch-Pfluger distortion function. In the past few years, the functions $\mu_{a}(r)$…
We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.
In the present paper, we establish necessary and sufficient conditions for the functions $x^\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert$ and $\alpha\bigl\lvert\psi^{(i)}(x+\beta)\bigr\lvert-x\bigl\lvert\psi^{(i+1)}(x+\beta)\bigr\lvert$…
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.
In this note we prove a condition of monotonicity for the integral functional $ F(g) = \int_a^b h(x)\, d[-g(x)] $ with respect to $g$, a function of bounded variation. This condition is applied to analyze the behavior of a generalized…