A Definition for Strong Rieszian Summability and its Relationship to Strong Cesaro Summability

Author:

Boyd A. V.,Hyslop J. M.

Abstract

1. Introduction. Given a series we define , by the relationsThe series Σan is said to be summable (C, k) to the sum s, ifas n→∞, and strongly summable (C, k), k>0, with index p, to the sum s, or summable [C; k, p] to the sum s, if

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. Hyslop J. M. , Proc., Glasgow Math. Assoc., I., p. 16.

2. Hardy G. H. and Riesz M. , The General Theory of Dirichlet Series (Cambridge Tract, No. 18), 27.

3. On the absolute summability of series by Rieszian means

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1. A Tauberian theorem for strong Abel summability type;Proceedings of the American Mathematical Society;1982

2. Über die starke Cesàro Summierbarkeit von Potenzreihen auf dem Rande des Konvergenzkreises;Mathematische Nachrichten;1974

3. On the strong N�rlund summability of a Cauchy product series;Mathematische Zeitschrift;1969

4. Multiplication theorems on strongly summable series;Proceedings of the American Mathematical Society;1966

5. An extension of a theorem on the equivalence between absolute Rieszian and absolute Cesàro summability;Proceedings of the Glasgow Mathematical Association;1959-07

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