ONE-SIDED TAUBERIAN CONDITIONS FOR THE ((N)over-bar, p) SUMMABILITY OF INTEGRALS


Totur U., Okur M. A. , ÇANAK İ.

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, vol.80, no.3, pp.65-74, 2018 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 80 Issue: 3
  • Publication Date: 2018
  • Title of Journal : UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
  • Page Numbers: pp.65-74

Abstract

Let p be a function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0; x) for 0 < x < infinity, in symbol: p is an element of L-loc(1) (R+) such that P (x) = integral(x)(0) p(t)dt not equal 0 for each x > 0, P (0) = 0 and P (x) -> infinity as x -> infinity. For a real-valued function f is an element of L-loc(1) (R+), we set s (x) := integral(0)(x) f (t)dt and sigma((1))(p) (x) := 1/P(x) integral(x)(0) s (t) p (t)dt; x > 0, provided that P (x) > 0.