Results 11 to 20 of about 28,850 (259)
Functional inequalities for the Bickley function [PDF]
Mathematical Inequalities & Applications, 2014 In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, Hölder-Rogers, Cauchy-Schwarz, Carlson and Grüss inequalities, as well as the monotone form of l'Hospital's rule.
Baricz, Árpád, Pogány, Tibor K.
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Inequalities for the Beta function [PDF]
Mathematical Inequalities & Applications, 2015 Let g(x):= (e/x)xΓ(x+1) and F(x,y):= g(x)g(y)/g(x+y). Let Dx,y (k) be the k th differential in Taylor's expansion of logF(x,y) . We prove that when (x,y) ∈ R+ 2 one has (-1)k-1Dx,y (k) (X,Y) > 0 for every X,Y ∈ R+, and that when k is even the conclusion holds for every X,Y ∈ R with (X,Y) = (0,0).
Grenié, Loic Andre Henri +1 more
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Journal of Mathematical Analysis and Applications, 1996 Given extended real numbers \(a,b\) with \(a0 ...
Simić, Slavko, Radenović, Stojan
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Testing functional inequalities [PDF]
Journal of Econometrics, 2013 60 pages, 4 ...
Sokbae (Simon) Lee +2 more
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Inequalities for Cyclic Functions
Journal of Approximation Theory, 2001 The cyclic functions are defined as the cyclic partial sums of the exponential function \[ \varphi_n(z):=\sum_{\nu=0}^\infty {z^{n\nu}\over (n\nu)!} \qquad (z\in {\mathbb C},\;2\leq n\in{\mathbb N}). \] In the special case \(n=2\), \(\varphi_2\) is the classical cosine hyperbolic function.
Alzer, H, Ruscheweyh, S, Salinas, L
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A note on a functional inequality
International Journal of Mathematics and Mathematical Sciences, 1992 We prove: If r1,…,rk are (fixed) positive real numbers with ∏j=1krj>1, then the only entire solutions φ:ℂ→ℂ of the functional inequality∏j=1k|φ(rjz)|≥(∏j=1krj)|φ(z)|kare φ(z)=czn, where c is a complex number and n is a positive integer.
Horst Alzer
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An Inequality for Convex Functions
Journal of Mathematical Analysis and Applications, 1994 The authors prove the following interesting inequality for convex functions: Suppose that positive numbers \(s_{i,j}\) \((i= 0,1,2; j= 1,\dots,n)\) satisfy \(s_{1,j}\leq s_{0,j}\leq s_{2,j}\) \((j= 1,\dots,n)\) and \(a_ j s^{-1}_{i,1}+ b_ j s^{-1}_{i,j}= 1\) \((i= 0,1,2; j= 2,\dots,n)\) for positive constants \(a_ j\), \(b_ j\) \((j= 2,\dots,n)\). If \(
Pearce, C.E.M., Pecaric, J.E.
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BMC Geriatrics, 2022 Background This study aims to determine the change of inequality in functional disability of older populations in China over the period from 2008 to 2018 and decompose the contribution of the personal and environmental predictors to the change.
Tao Zhang +3 more
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An inequality for bounded functions [PDF]
Mathematical Inequalities & Applications, 2014 In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
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An inequality for a quadratic functional
Vietnam Journal of Mechanics, 2009 An inequality is proved for a quadratic functional with the logarithmic kernel. The best constant of this inequality and the corresponding function for which the equality holds are found precisely.
Le Khanh Chau
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