On Tauberian conditions for the Hölder integrability method
Makaleler > Tam Makale · 2025
Yazarlar: Muhammet Ali Okur, İbrahim ÇANAK
Positivity, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2025, cilt 29, ss 1-11
DOI: 10.1007/s11117-025-01134-y
Özet
Abstract Let f be a real-valued continuous function on $$[0,\infty )$$ [ 0 , ∞ ) . Although every convergent integral $$s(x)=\int _0^xf(t)dt$$ s ( x ) = ∫ 0 x f ( t ) d t is (H, 1) summable, the converse-deducing convergence from (H, 1) summability-requires Tauberian conditions. In this study, we demonstrate that the slowly decreasing condition ( $$\mathcal{S}\mathcal{D}$$ S D ), which is more general than convergence, is sufficient to establish the convergence of integrals that are (H, 1) and (H, 2) summable. Our results extend the theorems in [1, 2] and introduce weaker Tauberian conditions applicable to (H, k) summability methods.