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Functional Inequalities in the Framework of Banach Spaces
Results in MathematicsThis paper aims to illustrate the usefulness of majorization theory and higher-order convexity in generalizing several classical inequalities as functional inequalities. This includes results due to Ball et al.
Constantin P. Niculescu
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, 2017
This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects.
T. Rajba
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This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects.
T. Rajba
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Some functional inequalities on non-reversible Finsler manifolds
Proceedings - Mathematical Sciences, 2017We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by Ohta and Sturm.
Shin-ichi Ohta
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Inequalities for Appell Functions
Journal of Mathematical Physics, 1970The asymptotic expansion of one of Appell's generalizations of the Jacobi function is given for one parameter becoming large while the other is kept fixed. Inequalities are given which may be useful when both parameters become large.
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On gamma function inequalities
Scandinavian Actuarial Journal, 1973Watson's method [1] is used to find two convergent monotonically non-decreasing sequences whose upper bounds are equal to Γ(l)Γ(l∓2a)/Γ2(l∓a) ( = K say), provided l > max (0, - 2a). Boyd [2] showed that Gurland's inequality [3] for K corresponds to the first term of the first sequence; Raja Rao's inequality [4] corresponds to the second term of the ...
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Characterization of Pinched Ricci Curvature by Functional Inequalities
, 2016In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, $$L^p$$Lp-inequalities and log-Sobolev ...
Lijuan Cheng, Anton Thalmaier
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Generalized Functional Inequalities
2014The Poincare, logarithmic Sobolev and Sobolev inequalities capture different features of the associated semigroup or the invariant measure, in terms of convergence to equilibrium, estimates on the heat kernels or tail behaviors of the invariant measure. This chapter investigates intermediate or more general families of functional inequalities which are
Dominique Bakry +2 more
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Advances in Computational Mathematics, 2009
The Gauss error function of a real variable is defined by \(\text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt\). Results on the error function may be found e.g., in the well-known monographs by Abramowitz-Stegun (1965), Gradshteyn-Ryzhik (1994), or Luke (1975).
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The Gauss error function of a real variable is defined by \(\text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt\). Results on the error function may be found e.g., in the well-known monographs by Abramowitz-Stegun (1965), Gradshteyn-Ryzhik (1994), or Luke (1975).
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Numerical Algorithms, 2008
Some new inequalities for Euler's gamma function are derived and proved.
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Some new inequalities for Euler's gamma function are derived and proved.
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