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Tauberian conditions connecting Cesaro and Riesz discrete means methods
Moscow University Mathematics Bulletin, 2012Let \(\left\{ a_{n},n\geq 0\right\} \) denote a sequence of real numbers. The series \(\sum a_{n}\) is summable to the real number \(S\) by the Cesàro method \( (C,\alpha )\) of order \(\alpha \) if \(A(n,\alpha )/E(n,\alpha )\rightarrow S\), where \(E(n,\alpha )=\binom{n+\alpha }{\alpha }\) and \(A(n,\alpha )=\sum_{m=0}^{n}E(n-m,\alpha )a_{m}\).
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Tauberian type gap conditions for Cesàro summation methods
Mathematical Notes, 1999Let \(P\) and \(Q\) be summation methods for numerical series. A condition \(R\) on a sequence \(\{a_n\}\) is called a \(T_Q(P)\)-condition if any \(P\)-summable series \(\sum a_n\) such that \(\{a_n\}\) satisfies \(R\) is \(Q\)-summable. A sequence \(\{a_n\}\) belongs to \((G,k)\) if there exist a natural number \(C\), a real number \(q>1\), and a ...
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Some Tauberian conditions obtained through weighted generator sequences
Georgian Mathematical Journal, 2014Abstract Recently, the concept of weighted generator sequence has been introduced by Çanak and Totur [Comput. Math. Appl. 62 (2011), no. 6, 2609–2615]. They proved that certain conditions in terms of weighted generator sequences are Tauberian conditions for the weighted mean method.
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Absolute tauberian conditions for absolute hausdorff and quasi-hausdorff methods
Israel Journal of Mathematics, 1970The purpose of this paper is to prove that for a large set of absolute Hausdorff and quasi-Hausdorff methods the condition $$\sum\limits_{k = 1}^\infty {\left| {\lambda _n a_n - \lambda _{n - 1} a_{n - 1} } \right|< } \infty $$ is a Tauberian condition, i.e., its fulfillment together with the absolute summability of\(\sum\limits_{n = 0}^\infty ...
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ON ONE-SIDED TAUBERIAN CONDITIONS
Analysis, 1983Bingham, N. H., Goldie, C. M.
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On tauberian conditions for (C, 1) summability of integrals
2019We investigate some Tauberian conditions in terms of the general control modulo of the oscillatory behavior of integer order of continuous real functions on [0, alpha) for (C, 1) summability of integrals. Moreover, we obtain a Tauberian theorem for a real bounded function on [0, alpha).
Çanak I., Totur U.
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WEAKENING TAUBERIAN CONDITIONS FOR SUMMABILITY METHODS
Analysis, 1989Dominikus Noll, Wolfgang Stadler
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Necessary and Sufficient Tauberian Condition for Both Cesàro and Abel Summability
Jahresbericht der Deutschen Mathematiker-VereinigungThe Weakly-Vanishing Mean Oscillation (W-VMO) property is introduced and its relation with some Tauberian conditions in the literature is investigated. Then, it is shown that this property is a necessary and sufficient condition under which convergence follows from Abel and Cesàro summability.
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