A Property of completely monotonic functions
نویسندگان
چکیده
منابع مشابه
A class of logarithmically completely monotonic functions
The main object of this work is to give some conditions for a class of functions to be logarithmically completely monotonic. Our result is shown to be an extension of a result which was proven in the recent literature on this subject. c © 2008 Elsevier Ltd. All rights reserved.
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We completely determine the set of (α, β) ∈ R2 for which the function e −e ex−1 is convex on (0,∞) and use this result to give some special classes of completely monotonic functions of positive order related to gamma and psi functions.
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We prove: (i) Let Fn(x) = Pn(x) [ e− ( 1 + 1 x )x] and Gn(x) = Pn(x) [( 1 + 1 x )x+1 − e ] , where Pn(x) = xn + ∑n−1 ν=0 cνx ν is a polynomial of degree n ≥ 1 with real coefficients. Fn is completely monotonic if and only if n = 1 and c0 ≥ 11/12; and Gn is completely monotonic if and only if n = 1 and c0 ≥ 1/12. (ii) The functions x 7→ e − (1 + 1/x)x and x 7→ (1 + 1/x)x+1 − e are Stieltjes tran...
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A function f : (0,∞) → R is said to be completely monotonic if (−1)nf (n)(x) ≥ 0 for all x > 0 and n = 0, 1, 2, .... In this paper we present several new classes of completely monotonic functions. Our functions have in common that they are defined in terms of the classical gamma, digamma, and polygamma functions. Moreover, we apply one of our monotonicity theorems to prove a new inequality for ...
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If, in addition, f(x) is continuous at x = a, then it is called completely monotonic over [a, b), with similar definitions for (a, b] and [a, b]. A function is absolutely monotonic if all its derivatives are non-negative. A detailed study of these concepts can be found, for example, in [11, Chapter IV]. Our chief concern here is for the standard case in which a = 0, b = + 00. For this, S. N. Be...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1987
ISSN: 0263-6115
DOI: 10.1017/s1446788700028160