منابع مشابه
Wallis Inequality with a Parameter
We introduce a parameter z for the well-known Wallis’ inequality, and improve results on Wallis’ inequality are proposed. Recent results by other authors are also improved.
متن کاملBest Upper Bounds Based on the Arithmetic-geometric Mean Inequality
In this paper we obtain a best upper bound for the ratio of the extreme values of positive numbers in terms of the arithmetic-geometric means ratio. This has immediate consequences for condition numbers of matrices and the standard deviation of equiprobable events. It also allows for a refinement of Schwarz’s vector inequality.
متن کاملOn the Best Sobolev Inequality
We prove that the best constant in the Sobolev inequality (WI,” c Lp* with $= f i and 1 c p < n) is achieved on compact Riemannian manifolds, or only complete under some hypotheses. We also establish stronger inequalities where the norms are to some exponent which seems optimal. 0 Elsevier, Paris
متن کاملBest Constant in Sobolev Inequality
The equality sign holds in (1) i] u has the Jorm: (3) u(x) = [a + btxI,~',-'] 1-~1~ , where Ix[ = (x~ @ ...-~x~) 1⁄2 and a, b are positive constants. Sobolev inequalities, also called Sobolev imbedding theorems, are very popular among writers in part ial differential equations or in the calculus of variations, and have been investigated by a great number of authors. Nevertheless there is a ques...
متن کاملThe Best Bounds in Gautschi-kershaw Inequalities
By employing the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma, psi and polygamma functions, and other analytic techniques, this note provides an alternative proof of a monotonicity and convexity property by N. Elezović, C. Giordano and J. Pečarić in [4] to establish the best bounds in GautschiKershaw inequalities. Moreover, some (...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07499-4