Necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic

Convolution Theorem ◽

Completely Monotonic ◽

In the paper, by convolution theorem for the Laplace transforms, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.

Monotonicity and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function

10.31219/osf.io/whb2q ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Convolution Theorem ◽

Monotonic Functions ◽

Completely Monotonic ◽

In the paper, by 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 author (1) presents the decreasing monotonicity of a ratio constituted via three derivatives of a function involving trigamma function; (2) discovers necessary and sufficient conditions for a function constituted via three derivatives of a function involving trigamma function to be completely monotonic. These results conform previous guesses posed by the author.

Complete monotonicity of a difference constituted by four derivatives of a function involving trigamma function

10.20944/preprints202011.0343.v1 ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Convolution Theorem ◽

Monotonic Functions ◽

Completely Monotonic ◽

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic.

Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm191111014q ◽

2021 ◽

pp. 14-14

Author(s):

Feng Qi

Keyword(s):

Exponential Function ◽

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Monotonic Functions ◽

Completely Monotonic ◽

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic. These results generalize corresponding known ones.

Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic

Mathematical Inequalities & Applications ◽

10.7153/mia-2021-24-58 ◽

2021 ◽

pp. 845-855

Author(s):

Feng Qi

Keyword(s):

Sufficient Conditions ◽

Completely Monotonic ◽

Monotonicity of a ratio involving trigamma and tetragamma functions

10.31219/osf.io/5rfb8 ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Sufficient Conditions ◽

Laplace Transforms ◽

Exponential Functions ◽

Monotonic Functions ◽

Completely Monotonic ◽

The Right ◽

Logarithmic Concavity

In the paper, by convolution theorem of the Laplace transforms, Bernstein's theorem for completely monotonic functions, and logarithmic concavity of a function involving exponential functions, the author(1) finds necessary and sufficient conditions for a ratio involving trigamma and tetragamma functions to be monotonic on the right real semi-axis;(2) and presents alternative proofs of necessary and sufficient conditions for a function and its negativity involving trigamma and tetragamma functions to be completely monotonic on the positive semi-axis.These results generalizes known conclusions recently obtained by the author.

COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972712001025 ◽

2013 ◽

Vol 88 (2) ◽

pp. 309-319 ◽

Cited By ~ 6

Author(s):

FENG QI ◽

PIETRO CERONE ◽

SEVER S. DRAGOMIR

Keyword(s):

Divided Difference ◽

Sufficient Conditions ◽

Complete Monotonicity ◽

Divided Differences ◽

Psi Function ◽

Gamma Functions ◽

Completely Monotonic ◽

Polygamma Functions ◽

AbstractNecessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.

Stochastic Orders in Terms of Laplace Transforms

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319950306 ◽

1995 ◽

Vol 45 (3-4) ◽

pp. 195-202 ◽

Cited By ~ 2

Author(s):

Asok K. Nanda

Keyword(s):

Laplace Transform ◽

Sufficient Conditions ◽

Laplace Transforms ◽

Stochastic Orders ◽

Partial Orderings ◽

Life Distributions ◽

Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.

Lower Bound of Sectional Curvature of Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions

10.20944/preprints202011.0315.v1 ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Lower Bound ◽

Sectional Curvature ◽

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Convolution Theorem ◽

Open Problems ◽

Polygamma Functions ◽

Beta Distributions ◽

In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.

Necessary and sufficient conditions for functions involving the psi function to be completely monotonic

Journal of Inequalities and Applications ◽

10.1186/s13660-015-0674-8 ◽

2015 ◽

Vol 2015 (1) ◽

Cited By ~ 5

Author(s):

Zhen-Hang Yang ◽

Yu-Ming Chu ◽

Xiao-Hui Zhang

Keyword(s):

Sufficient Conditions ◽

Psi Function ◽

Completely Monotonic ◽

Fourier-Laplace transforms decaying exponentially

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100064896 ◽

1988 ◽

Vol 103 (2) ◽

pp. 321-322

Author(s):

H. Kaneta

Keyword(s):

Laplace Transform ◽

Positive Measure ◽

Sufficient Conditions ◽

Laplace Transforms ◽

Image Position ◽

Let ƒ(x) be a C-valued function which is integrable with respect to a positive measure m on the Borel σ-field of R = (– ∞, ∞). We shall give necessary and sufficient conditions under which the following Fourier-Laplace transform f(λ) of ƒ(x) decays exponentially as λ → ∞:where θ is a constant with –π/2 ≤ θ ≤ π/2.