On the integrals of Perron type-Reference-Cited by-同舟云学术

On the integrals of Perron type

Published:1973 Issue:0 Volume:182 Page:481-501
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Bullen P. S.,Lee C. M.

Abstract

An abstract derivate system is defined axiomatically, and then a naturally corresponding Perron integral theory is developed, unifying all the existing integral theories of Perron type of first order. A new scale of approximately mean-continuous integrals and a new scale of symmetric Cesàro-Perron integrals are obtained as examples of the general theory. Also, the MZ-integral and the SCP-integral are proved to be equivalent.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1973-182-00/S0002-9947-1973-0338291-6/S0002-9947-1973-0338291-6.pdf

Reference30 articles.

1. A property of Cesàro-Perron integrals;Bosanquet, L. S.;Proc. Edinburgh Math. Soc. (2),1940

2. The 𝑃ⁿ-integral;Bullen, P. S.;J. Austral. Math. Soc.,1972

3. J. C. Burkill, The Cesàro-Perron integral, Proc. London Math. Soc. (2) 34 (1932), 314-322.

4. \bysame, The Cesàro-Perron scale of integration, Proc. London Math. Soc. (2) 39 (1935), 541-552.

5. Integrals and trigonometric series;Burkill, J. C.;Proc. London Math. Soc. (3),1951

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