Tauberian theorems for the weighted mean method of summability of integrals


ÇANAK İ. , Ozsarac F.

3rd International Conference of Mathematical Sciences (ICMS), İstanbul, Turkey, 4 - 08 September 2019, vol.2183 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2183
  • Doi Number: 10.1063/1.5136127
  • City: İstanbul
  • Country: Turkey

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)(t)dt # 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