Remarks on some completely monotonic functions
نویسندگان
چکیده
منابع مشابه
Some completely monotonic functions of positive order
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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In this paper, some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.
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Complete monotonicity properties of some functions involving the psi function are studied and some known results are extended and generalized. Moreover, a necessary and sufficient conditions for some functions to be completely monotonic are presented and proved. Mathematics subject classification (2010): 33B15, 26D15.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.12.017