Geodesic
Some Remarks Concerning (f, dn ) and [F, dn ] Summability Methods
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1361-1365

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we note a simple connection between the (ƒ, dn) method of summability (defined by Smith (8)) and a composition of [F, dn] (defined by Jakimovski (4)) and Sonnenschein methods (9; 10). This connection is then used to supply some sufficient conditions for the regularity of (ƒ, dn) methods by using known regularity conditions for various [F, dn] and Sonnenschein methods. Finally, the connection is further exploited to obtain information about the Lebesgue constants for a certain class of [F, dn] methods by investigating related (ƒ, dn) methods. 2. Definitions and the regularity theorem. The (ƒ, dn) method of summability is defined by Smith (8) essentially as follows. Letƒ(z) be a nonconstant entire function satisfying ƒ (l) = 1 and let {dn} be a sequence of complex numbers satisfying dt ≠ – 1, di ≠ – ƒ(0) (i ≧ 1). 
Koch, C. F. Some Remarks Concerning (f, dn ) and [F, dn ] Summability Methods. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1361-1365. doi: 10.4153/CJM-1969-150-7
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