TAUBERIAN THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY OF INTEGRALS


Ozsarac F., ÇANAK İ.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, vol.35, no.3, pp.775-788, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.22190/fum12003775o
  • Title of Journal : FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
  • Page Numbers: pp.775-788

Abstract

Let q be a positive weight function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0, x) for 0 < x < infinity, in symbol: q is an element of L-loc(1)(R+) such that Q(x) := integral(x)(0) q(t)dt not equal 0 for each x > 0, Q(0) = 0 and Q(x) -> infinity as x -> infinity. Given a real or complex-valued function f is an element of L-loc(1) (R+), we define s(x) := integral(x)(0) f (t)dt and