On the convergence of weighted mean summable improper integrals over $${\mathbb {R}}_{\ge 0}$$
Makaleler > Tam Makale · 2022
Yazarlar: Sefa Anıl Sezer, İbrahim ÇANAK
The Journal of Analysis, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Scopus, 2022, cilt 31, ss 1029-1039
DOI: 10.1007/s41478-022-00501-2
Özet
Given a real-valued function a(x) which is locally integrable in the sense of Lebesgue over R≥ 0, we obtain Tauberian conditions for the convergence of the integral ∫0∞a(t)dt out of the weighted mean summability. Furthermore, we discuss summability of improper integrals via iterations of weighted means and provide corresponding Tauberian theorems.