“Copson's Inequality”的概念、定义、习题解题方法及翻译-数学辞典

单词

Copson's Inequality

释义

Copson's Inequality

Let be a Nonnegative Sequence and a Nonnegative integrable function. Define

			(1)
			(2)

and

			(3)
			(4)

and take

. For integrals,

(5)

(unless

is identically 0). For sums,

(6)

(unless all

References

Beesack, P. R. ``On Some Integral Inequalities of E. T. Copson.'' In General Inequalities 2 (Ed. E. F. Beckenbach). Basel: Birkhäuser, 1980.

Copson, E. T. ``Some Integral Inequalities.'' Proc. Royal Soc. Edinburgh 75A, 157-164, 1975-1976.

Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Theorems 326-327, 337-338, and 345 in Inequalities. Cambridge, England: Cambridge University Press, 1934.

Mitrinovic, D. S.; Pecaric, J. E.; and Fink, A. M. Inequalities Involving Functions and Their Integrals and Derivatives. Dordrecht, Netherlands: Kluwer, 1991.

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