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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, Andrea Laforgia, Necdet Batir, Qiu-Ming Luo   +3 more
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Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function

Demonstratio Mathematica
In 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   +3 more sources

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
doaj   +1 more source

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.
Taghavian, Hamed, Drummond, Ross, Johansson, Mikael   +2 more
openaire   +3 more sources

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
doaj   +1 more source

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   +1 more source

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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Dunkl completely monotonic functions [PDF]

Journal of Difference Equations and Applications, 2017
We introduce the notion of Dunkl completely monotonic functions on $\left(- , \right), >0$. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.
Khaled Mehrez, Jamel El Kamel
openaire   +2 more sources

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
doaj   +1 more source