Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Absolute Tauberian constants for Cesàro means of a function
HTML articles powered by AMS MathViewer

by Soraya Sherif PDF
Trans. Amer. Math. Soc. 224 (1976), 231-242 Request permission

Abstract:

This paper is concerned with introducing two estimates of the forms $F \leqslant C{A_k}(\alpha ),F \leqslant D{B_k}(\alpha ),(\alpha > 0)$, where $F = \smallint _0^\infty {|d\{ f(\alpha x) - {\sigma _k}(x)\} |,{\sigma _k}(x)}$ denote the Cesàro transform of order k of the function $f(x) = \smallint _0^x {g(t)\;dt,g(t)}$ is a function of bounded variation in every finite interval of $t \geqslant 0,{A_k}(\alpha ),{B_k}(\alpha )$ are absolute Tauberian constants, $C = \smallint _0^\infty {|d\{ tg(t)\} | < \infty ,D = \smallint _0^\infty {|d\{ \phi (t)\} | < \infty } }$ and $\phi (t) = {t^{ - 1}}\smallint _0^t {ug(u)du}$. The constants ${A_k}(\alpha ),{B_k}(\alpha )$ will be determined.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 40D10
  • Retrieve articles in all journals with MSC: 40D10
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 224 (1976), 231-242
  • MSC: Primary 40D10
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0420059-6
  • MathSciNet review: 0420059