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On quasi-monotone sequences and their applications

Published online by Cambridge University Press:  17 April 2009

Hüseyin Bor
Affiliation:
Department of Mathematics, Erciyes University, Kayseri 38039, Turkey
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Abstract

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In this paper using δ-quasi-monotone sequences a theorem on summability factors of infinite series, which generalises a theorem of Mazhar [7] on |C, 1|k summability factors of infinite series, is proved. Also we apply the theorem to Fourier series.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Boas, R.P. Jr., ‘Quasi-positive sequences and trigonometric series’, Proc. Land. Math. Soc. 14(A) (1965), 3846.CrossRefGoogle Scholar
[2]Bor, H., ‘On two summability methods’, Math. Proc. Camb. Philos. Soc. 97 (1985), 147149.CrossRefGoogle Scholar
[3]Chen, K.K., ‘Functions of bounded variation and Cesàro means of Fourier series’, Acad. Sinica Sc. Records 1 (1954), 283289.Google Scholar
[4]Flett, T.M., ‘On an extension of absolute summability and some theorems of Littlewood and Paley’, Proc. Land. Math. Soc. 7 (1957), 113141.CrossRefGoogle Scholar
[5]Hardy, G.H., Divergent Series (Oxford University Press, 1949).Google Scholar
[6]Kogbetliantz, E., ‘Sur les séries absolument sommables par la méthode des moyennes arithmétiques’, Bull. Sci. Math. 40 (1925), 234256.Google Scholar
[7]Mazhar, S.M., ‘On generalized quasi-convex sequence and its applications’, Indian J. Pure Appl. Math. 8 (1977), 784790.Google Scholar