A PROPERTY OF LOGARITHMICALLY ABSOLUTELY MONOTONIC FUNCTIONS AND THE LOGARITHMICALLY COMPLETE MONOTONICITY OF A POWER-EXPONENTIAL FUNCTION

By Feng Qi (祁锋), Bai-Ni Guo (郭白妮). 2009

87 citations recorded by the source corpus.

In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the function $\bigl(1+\frac{\alpha}x\bigr) ^{x+\beta}$ are proved, where $\alpha$ and $\beta$ are given real parameters, a new proof for the inclusion that a logarithmically completely monotonic function is also completely monotonic is given, and an open problem is posed.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c3028444c207dbfc6b37b65f7849d886d27c0027

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In Applied Mathematics

Citations in the corpus

Some properties of functions related to the gamma and psi functions (2010, methodology): “We begin by listing some necessary definitions and preliminaries which can be found in [ 9 , Chapter XIII; 11 ; 13 ; 21 ; 24 , Chapter IV].”
A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application (2006, unknown): “…function f on [0,∞) is a Laplace transform of the measure µ. Recall also [5, 46, 49] that a positive function f is called logarithmically completely monotonic on an interval I if f has derivatives of all orders on I and its logarithm ln f satisfies (−1)k[ln f(x)](k) ≥ 0 (3) for all k ∈ N on I.”