Results 1 to 10 of about 3,749,896 (217)
Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions [PDF]
Sahand Communications in Mathematical Analysis, 2022 We extend the definitions of $\nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $\int P(y)f(y) dy$ and $\int \int P(y,z) f(y,z) dy dz$ are deduced.
Faraz Mehmood, Asif Khan, Muhammad Adnan
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A class of completely monotonic functions involving the polygamma functions
Journal of Inequalities and Applications, 2022 Let Γ ( x ) $\Gamma (x)$ denote the classical Euler gamma function. We set ψ n ( x ) = ( − 1 ) n − 1 ψ ( n ) ( x ) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$ ( n ∈ N $n\in \mathbb{N}$ ), where ψ ( n ) ( x ) $\psi ^{(n)}(x)$ denotes the nth derivative of the
Li-Chun Liang, Li-Fei Zheng, Aying Wan
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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
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A SOLUTION TO FOURTH QI’S CONJECTURE ON A COMPLETE MONOTONICITY
Проблемы анализа, 2020 In the paper, a complete monotonicity for some function is proved. This problem was posted by F. Qi and R.P.
L. Matej´ıcka
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Higher Monotonicity Properties for Zeros of Certain Sturm-Liouville Functions
Mathematics, 2023 In this paper, we consider the differential equation y″+ω2ρ(x)y=0, where ω is a positive parameter. The principal concern here is to find conditions on the function ρ−1/2(x) which ensure that the consecutive differences of sequences constructed from the ...
Tzong-Mo Tsai
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Two Approximation Formulas for Bateman’s G-Function with Bounded Monotonic Errors
Mathematics, 2022 Two new approximation formulas for Bateman’s G-function are presented with strictly monotonic error functions and we deduced their sharp bounds. We also studied the completely monotonic (CM) degrees of two functions involving G(r), deducing two of its ...
Mansour Mahmoud, Hanan Almuashi
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On a Conjecture of Alzer, Berg, and Koumandos
Mathematics, 2020 In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ (
Ladislav Matejíčka
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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
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Arab Journal of Basic and Applied Sciences, 2021 In the paper, the author presents bounds 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 degrees of remainders of ...
Feng Qi
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A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function
Journal of Inequalities and Applications, 2010 We show that the function is strictly logarithmically completely monotonic on if and only if and is strictly logarithmically completely monotonic on if and only if .
Zhao Tie-Hong, Chu Yu-Ming
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