TAUBERIAN CONDITIONS FOR q-CESARO INTEGRABILITY


SEZER S. A. , ÇANAK İ.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, cilt.35, ss.471-483, 2020 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 35 Konu: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.22190/fumi2002471s
  • Dergi Adı: FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
  • Sayfa Sayıları: ss.471-483

Özet

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.