On the convergence of weighted mean summable improper integrals over $${\mathbb {R}}_{\ge 0}$$
Articles > Article · 2022
Authors: Sefa Anıl Sezer, İbrahim ÇANAK
The Journal of Analysis, Journal Indexed in SCI Expanded, International, Scopus, 2022, vol 31, pp 1029-1039
DOI: 10.1007/s41478-022-00501-2
Summary
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.