منابع مشابه
An Ostrowski-Grüss type inequality on time scales
for all x ∈ [a, b]. This inequality is a connection between the Ostrowski inequality [12] and the Grüss inequality [13]. It can be applied to bound some special mean and some numerical quadrature rules. For other related results on the similar integral inequalities please see the papers [6, 10, 11, 14] and the references therein. The aim of this paper is to extend a generalizations of Ostrowski...
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Integration with weight functions is used in countless mathematical problems such as: approximation theory and spectral analysis, statistical analysis and the theory of distributions. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Barnett et al. in 2001 and Rafiq et al. in 2006. We also discuss some other interesting inequaliti...
متن کاملNote 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 − ...
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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...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2005
ISSN: 1331-4343
DOI: 10.7153/mia-08-23