TAUBERIAN CONDITIONS FOR q-CESARO INTEGRABILITY


SEZER S. A. , ÇANAK İ.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, vol.35, no.2, pp.471-483, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.22190/fumi2002471s
  • Title of Journal : FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
  • Page Numbers: pp.471-483

Abstract

Given a q-integrable function f on [0, infinity), we define s(x) = integral(x)(0) f (t)d(q)t and sigma(s(x)) = 1/x integral(x)(0) s(t)d(q)t for x > 0. It is known that if lim(x ->infinity) s(x) exists and is equal to A, then lim(x ->infinity) sigma(s(x)) = A. But the converse of this implication is not true in general. Our goal is to obtain Tauberian conditions imposed on the general control modulo of s(x) under which the converse implication holds. These conditions generalize some previously obtained Tauberian conditions.