Absolute Cesàro summability of orthogonal series
نویسندگان
چکیده
منابع مشابه
On absolute generalized Norlund summability of double orthogonal series
In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...
متن کاملOn generalized absolute Cesàro summability
In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.
متن کاملOn absolute matrix summability of orthogonal series
In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerica...
متن کاملFactors 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...
متن کاملqn|k summability of orthogonal series
In this paper we obtain some sufficient conditions on |N, pn, qn|k summability of an orthogonal series. These conditions are expressed in terms of the coefficients of the orthogonal series. Also, several known and new results are deduced as corollaries of the main results. c ©2014 All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1953
ISSN: 0040-8735
DOI: 10.2748/tmj/1178245351