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On Scales of Summability Methods
Author(s) -
Kiesel Rüdiger
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951760110
Subject(s) - mathematics , abelian and tauberian theorems , convexity , power series , class (philosophy) , series (stratigraphy) , type (biology) , product (mathematics) , pure mathematics , algebra over a field , calculus (dental) , mathematical analysis , geometry , medicine , paleontology , ecology , dentistry , artificial intelligence , computer science , financial economics , economics , biology
Abstract In this paper we consider generalized Nörlund methods ( N αp ), α > ‐1, power series methods ( J p ) and the iteration product of two such methods. A particular case is that of the Cesaro means (C α ) with corresponding power series method ( A ), i.e., Abel's method. We obtain generalizations of inclusion, and tauberian and convexity theorems which are well‐known for the Cesàro‐Abel case, for a rich class of methods of the above type.