Abstract
In this paper, we investigate the asymptotic properties of the following integral for $\lambda\to\infty$ or for $\lambda\to 0^+$: $$ \int_0^{\delta} f(t) g(\lambda t)\,dt\qquad (\lambda>0). $$ Our results give another format of [CC, Theorem 1.1]. They give some information for Riemann summability, and generalize Hobson [H], Karamata's Tauberian Theorem, [BGT, Proposition 4.3.1b], Aljan\v ci\'c-Bojani\'c-Tomi\'c [ABT], Bojanic-Karamata [BK], and Arandelovi\'c [A].