TAUBERIAN THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY OF INTEGRALS
Articles > Article · 2020
Authors: Firat Ozsarac, İbrahim ÇANAK
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, Journal Indexed in SCI Expanded, International, 2020, vol 35, pp 775-788
Summary
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