Results 41 to 50 of about 10,784,145 (367)

A complete monotonicity property of the multiple gamma function

Comptes Rendus. Mathématique, 2020
We consider the following functions \[ f_n(x)=1-\ln x+\frac{\ln G_n(x+1)}{x} \text{ and }g_n(x)=\frac{\@root x \of {G_n(x+1)}}{x},\; x\in (0,\infty ),\; n\in \mathbb{N}, \] where $G_n(z)=\left(\Gamma _n(z)\right)^{(-1)^{n-1}}$ and $\Gamma _n$ is the ...
Das, Sourav
doaj   +1 more source

Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function

Journal of Inequalities and Applications, 2021
In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q ( x + 1 ) / Γ q ( x + s ) ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ for all real number s and 0 < q ≠ 1 $0< q\neq1$ in terms of the q-digamma function.
Faris Alzahrani, Ahmed Salem, Moustafa El-Shahed   +2 more
doaj   +1 more source

The Adaptive Quadratic Linear Unit (AQuLU): Adaptive Non Monotonic Piecewise Activation Function

Tehnički Vjesnik, 2023
The activation function plays a key role in influencing the performance and training dynamics of neural networks. There are hundreds of activation functions widely used as rectified linear units (ReLUs), but most of them are applied to complex and large ...
Zhandong Wu, Haiye Yu, Lei Zhang, Yuanyuan Sui   +3 more
doaj   +1 more source

ON SEQUENCES OF MONOTONE FUNCTIONS [PDF]

Real Analysis Exchange, 1998
Several kinds of convergence (including pointwise, monotone, a.c., uniform, $\ldots$) in the family of monotone functions are ...
openaire   +3 more sources

Some integral inequalities for operator monotonic functions on Hilbert spaces

Special Matrices, 2020
Let f be an operator monotonic function on I and A, B∈I (H), the class of all selfadjoint operators with spectra in I. Assume that p : [0.1], →ℝ is non-decreasing on [0, 1].
Dragomir Silvestru Sever
doaj   +1 more source

n-Monotone exact functionals

Journal of Mathematical Analysis and Applications, 2008
We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and
de Cooman, Gert, Troffaes, Matthias, Miranda, Enrique   +2 more
openaire   +5 more sources

Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind

Comptes Rendus. Mathématique, 2023
In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function $-T_{\nu ,\alpha ,\beta }(s)$ is completely monotonic in $s$ and absolutely monotonic in $\nu $ if and only if $\beta \ge 1 ...
Mao, Zhong-Xuan, Tian, Jing-Feng
doaj   +1 more source

On monotonous separately continuous functions [PDF]

Applied General Topology, 2019
<p>Let T = (<strong>T</strong>, ≤) and T₁= (<strong>T</strong>₁ , ≤₁) be linearly ordered sets and X be a topological space.  The main result of the paper is the following: If function ƒ(t,x) : <strong>T</strong> × X → <strong>T< ...
openaire   +6 more sources

A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions [PDF]

, 2012
In this paper, we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite. We present some properties and relationships involving logarithmically completely monotonic functions and ...
Jamel El Kamel, K. Mehrez
semanticscholar   +1 more source

Some completely monotonic functions involving the polygamma functions

Journal of Inequalities and Applications, 2019
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
Peng Gao
doaj   +1 more source