Abstract
In this paper, by using an almost increasing and δ-quasi-monotone sequence, a general theorem on φ- ¦ C, α ¦ k summability factors, which generalizes a result of Bor [3] on φ ¦C, 1¦ k summability factors, has been proved under weaker and more general conditions.
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References
Aljancic S and Arandelovic D, O-regularly varying functions,Publ. Inst. Math. 22 (1977) 5–22
Balcı M, Absolute φ-summability factors,Comm. Fac. Sci. Univ. Ankara A 129 (1980) 63–80
Boas R P, Quasi-positive sequences and trigonometric series,Proc. London Math. Soc. A14 (1965) 38–46
Bor H, Absolute summability factors,Atti Sem. Mat. Fis. Univ. Modena 39 (1991) 419–422
Bosanquet L S, A mean value theorem,J. London Math. Soc. 16 (1941) 146–148
Flett T M, On an extension of absolute summability and some theorems of Littlewood and Paley,Proc. London Math. Soc. 7 (1957) 113–141
Flett T M, Some more theorems concerning the absolute summability of Fourier series,Proc. London Math. Soc. 8 (1958) 357–387
Pati T, The summability factors of infinite series,Duke Math. J. 21 (1954) 271–284
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Özarslan, H.S. A note on absolute summability factors. Proc. Indian Acad. Sci. (Math. Sci.) 113, 165–169 (2003). https://doi.org/10.1007/BF02829765
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DOI: https://doi.org/10.1007/BF02829765