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Completely Monotonic and Related Functions: Their Applications [PDF]
Journal of Applied Mathematics, 2014 Completely monotonic and related functions are important function classes inmathematical analysis. It was Bernstein [1] who in 1914 first introduced the notion of completely monotonic function. This year we celebrate its 100th anniversary. In 1921, Hausdorff [2] gave the notion of completely monotonic sequence, which is related to the notion of ...
Senlin Guo +3 more
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Logarithmically completely monotonic rational functions
Automatica, 2023 This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking.
Hamed Taghavian, Ross Drummond
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A Class of Logarithmically Completely Monotonic Functions and Their Applications [PDF]
Journal of Applied Mathematics, 2014 We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.
Senlin Guo
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A class of logarithmically completely monotonic functions
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Senlin Guo, H M Srivastava
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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
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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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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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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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