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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On determination of best-possible constants in integral inequalities involving derivatives


Author: Beny Neta
Journal: Math. Comp. 35 (1980), 1191-1193
MSC: Primary 26D15; Secondary 46E30, 65J99
MathSciNet review: 583496
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Abstract: This paper is concerned with the numerical approximation of the best possible constants $ {\gamma _{n,k}}$ in the inequality

$\displaystyle {\left\Vert {{F^{(k)}}} \right\Vert^2} \leqslant \gamma _{n,k}^{ ... ...ft\Vert F \right\Vert}^2} + {{\left\Vert {{F^{(n)}}} \right\Vert}^2}} \right\},$

where

$\displaystyle {\left\Vert F \right\Vert^2} = \int _0^\infty \vert F(x){\vert^2}\;dx.$

A list of all constants $ {\gamma _{n,k}}$ for $ n \leqslant 10$ is given.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0583496-X
PII: S 0025-5718(1980)0583496-X
Article copyright: © Copyright 1980 American Mathematical Society