Characterization of Absolute Summability Factors

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منابع مشابه

Characterization on Some Absolute Summability Factors of Infinite Series

A general theorem concerning some absolute summability factors of infinite series is proved. This theorem characterizes as well as generalizes our previous result [4]. Other results are also deduced.

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A note on absolute summability factors

A sequence (bn) of positive numbers is said to be δ -quasi-monotone, if bn → 0, bn > 0 ultimately and ∆bn ≥ −δn, where (δn) is a sequence of positive numbers (see [3]). Let (φn) be a sequence of complex numbers and let ∑an be a given infinite series with partial sums (sn). We denote by σα n and tα n the nth Cesàro means of order α , with α > −1, of the sequences (sn) and (nan), respectively, i.e.,

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Factors for generalized absolute Cesàro summability

A positive sequence (bn) is said to be almost increasing if there exists a positive increasing sequence cn and two positive constants A and B such that Acn ≤ bn ≤ Bcn (see [1]). Obviously every increasing sequence is almost increasing but the converse need not be true as can be seen from the example bn = ne(−1) n . Let ∑ an be a given infinite series with partial sums (sn). We denote by tn n-th...

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 1995

ISSN: 0022-247X

DOI: 10.1006/jmaa.1995.1373