Zur Korrespondenz zweier Klassen von Limitierungsverfahren

Ullrich, Egon

doi:10.1007/bf01283846

Cited by 2 publications

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“…Since the reverse of a (JV, p n ) method is (N, p n ), it follows that a matrix is both (N, p n ) and Hausdorff if and only if the matrix of the reverse transformation is both Norlund and Hausdorff. The result of Theorem 5 can then be deduced directly from the results of [1] and [16].…”

Section: Corollary 2 Let {P N } Be a Positive Non-decreasing Sequencmentioning

confidence: 99%

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Relations between (N, p_n) and (, p_n) summability

Kuttner

Rhoades

1968

Proceedings of the Edinburgh Mathematical Society

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Let {p n } be a positive sequence. The Norlund transformation (N, p n ) maps the sequence {s n } into the sequence {t n } by means of the equationThe transformation (JV, p^) maps a sequence {J B } into the sequence {«"} by means of the equation 1 "A matrix method is said to be regular if it is limit preserving for convergent sequences. Necessary and sufficient conditions for the regularity of (1) and (2) are, respectively,/^ = o(P n ) and J°n-» + oo.Let A and B denote two regular matrix methods, and A n (x) = I, k a nk x k , the nth transform of a sequence x, We say that B is stronger than A if A n {x)^l implies B n {x)-+l, I finite.If (3) continues to hold for / = ± oo, we say that B is totally stronger than A (written B t.s. A).The purposes of this paper are to extend the theorems of [8] to total comparison, and to establish additional properties between the two methods of summability.For completeness we quote the theorems from [8].

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Section: Corollary 2 Let {P N } Be a Positive Non-decreasing Sequencmentioning

confidence: 99%

“…Ullrich [16] showed that the only Norlund matrices which are also Hausdorff matrices are the Cesaro matrices. Agnew re-proved this result in [1].…”

Section: Corollary 2 Let {P N } Be a Positive Non-decreasing Sequencmentioning

confidence: 99%