A SOLUTION TO QI’S EIGHTH OPEN PROBLEM ON COMPLETE MONOTONICITY
Проблемы анализа, 2021 n this paper, the complete monotonicity of 1/( arctan 𝑥) is proved. This problem was posted by F. Qi and R. P. Agarwal as the eighth open problem of collection of eight open problems.
A. Venkata Lakshmi
doaj +2 more sources
Logarithmically Complete Monotonicity Properties Relating to the Gamma Function [PDF]
Abstract and Applied Analysis, 2011 We prove that the function fα,β(x)=Γβ(x+α)/xαΓ(βx) is strictly logarithmically completely monotonic on (0,∞) if (α,β)∈{( α,β):1/α≤β≤1, α≠1}∪{(α,β ...
Tie-Hong Zhao, Yu-Ming Chu, Hua Wang
doaj +2 more sources
Complete monotonicity related to the k-polygamma functions with applications [PDF]
Advances in Difference Equations, 2019 In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
doaj +2 more sources
Complete monotonicity involving some ratios of gamma functions [PDF]
Journal of Inequalities and Applications, 2017 In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic.
Zhen-Hang Yang, Shen-Zhou Zheng
doaj +2 more sources
On Some Complete Monotonicity of Functions Related to Generalized k−Gamma Function [PDF]
Journal of Mathematics, 2021 In this paper, we presented two completely monotonic functions involving the generalized k−gamma function Γkx and its logarithmic derivative ψkx, and established some upper and lower bounds for Γkx in terms of ψkx.
Hesham Moustafa +2 more
doaj +2 more sources
Monotonicity properties and bounds for the complete p-elliptic integrals [PDF]
Journal of Inequalities and Applications, 2018 We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
Ti-Ren Huang +3 more
doaj +2 more sources
Complete Monotonicity of Special Functions [PDF]
, 2015 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 $\left(-\frac{1}{x}\right)^{m}\frac{d^{k}}{dx^{k}}\left(x^{k+m}\frac{d^{m}}{dx^{m}}\left(\frac{f'(x)}{f(x)}\right)\right)$ is completely monotonic on $(0,\infty ...
R. Zhang
openalex +3 more sources
Extension of complete monotonicity results involving the digamma function
Moroccan Journal of Pure and Applied Analysis, 2018 By using some analytical techniques, we prove a complete monotonicity property of a certain function involving the (p, k)-digamma function. Subsequently, we derive some inequalities for the (p, k)- digamma function.
Nantomah Kwara
doaj +2 more sources
Monotonicity and complete monotonicity for continuous-time Markov chains [PDF]
Comptes Rendus. Mathématique, 2006 We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in ...
Paolo Dai Pra +2 more
openalex +6 more sources
Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function [PDF]
Demonstratio MathematicaIn this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
doaj +2 more sources