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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some regularity conditions for the $(f, d_{n}, z_{1})$ summability method


Authors: A. Jakimovski and H. Skerry
Journal: Proc. Amer. Math. Soc. 24 (1970), 281-287
MSC: Primary 40.31
DOI: https://doi.org/10.1090/S0002-9939-1970-0251399-1
MathSciNet review: 0251399
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Abstract | References | Similar Articles | Additional Information

Abstract: Regularity conditions for the generalized Lototsky summability method $(f,\;{d_n},\;{z_1})$ are derived which do not restrict the Taylor coefficients of $f$. Some examples are given.


References [Enhancements On Off] (What's this?)

  • Bogdan M. BajĆĄanski, Sur une classe gĂ©nĂ©rale de procĂ©dĂ©s de sommations du type d’Euler-Borel, Acad. Serbe Sci. Publ. Inst. Math. 10 (1956), 131–152 (French). MR 84605
  • J. Clunie and P. Vermes, Regular Sonnenschein type summability methods, Acad. Roy. Belg. Bull. Cl. Sci. (5) 45 (1959), 930–954. MR 125371
  • Amnon Jakimovski, A generalization of the Lototsky method of summability, Michigan Math. J. 6 (1959), 277–290. MR 130500
  • A. V. LotockiÄ­, On a linear transformation of sequences and series, Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Nauki 4 (1953), 61–91 (Russian). MR 0077668
  • Gaston Smith, On the $(f,\,d_{n})$-method of summability, Canadian J. Math. 17 (1965), 506–526. MR 176265, DOI https://doi.org/10.4153/CJM-1965-051-1
  • ---, A generalization of the $(f,\;{d_n})$ method of summability, Notices Amer. Math. Soc. 12 (1965), 599, abstract #625-180.

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Keywords: Regularity conditions, summability methods
Article copyright: © Copyright 1970 American Mathematical Society