منابع مشابه
Note on an Iyengar type inequality
Using Hayashi's inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezovi´c, J. Pečari´c, Steffensen's inequality and estimates of error in trapezoidal rule, Appl. In 1938 Iyengar proved the following inequality in [1]: Theorem 1. Let function f be differentiable on [a, b] and | f (x)| ≤ M. Then 1 b − ...
متن کاملOn an Iyengar-type inequality involving quadratures in n knots
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this short note, we give an Iyengar-type inequality involving quadratures in n knots, where n is an arbit...
متن کاملA Note on Perelman’s Lyh Type Inequality
We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the known differential inequalities of Li-Yau-Hamilton type via monotonicity formulae.
متن کاملNote on weighted Carleman-type inequality
In (1.2), letting p → ∞, then the following Carleman inequality [6, page 249] is deduced: ∞ ∑ n=1 ( a1a2 ···an )1/n < e ∞ ∑ n=1 an, (1.3) where an ≥ 0 for n∈N and 0 < ∑∞ n=1 an <∞. The constant e is the best possible. Carleman’s inequality (1.3) was generalized in [6, page 256] by Hardy as follows. Let an ≥ 0, λn > 0, Λn = ∑n m=1 λm for n∈N, and 0 < ∑∞ n=1 λnan <∞, then ∞ ∑ n=1 λn ( a1 1 a λ2 2...
متن کاملNote on an Inequality of Wegner
G. Wegner [12] gave a geometric characterization of all so–called Groemer packing of n ≥ 2 unit discs in E2 that are densest packings of n unit discs with respect to the convex hull of the discs. In this paper we provide a number theoretic characterization of all n satisfying that such a “Wegner packing” of n unit discs exists, and show that the proportion of these n is 23 24 among all natural ...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2006
ISSN: 0893-9659
DOI: 10.1016/j.aml.2005.08.018