Đurčić, Dragan; Božin, Vladimir A proof of an Aljančić hypothesis on \({\mathcal O}\)-regularly varying sequences. (English) Zbl 0946.26002 Publ. Inst. Math., Nouv. Sér. 62(76), 46-52 (1997). The relations of regularly varying sequences and regularly varying functions are known by the paper of R. Bojanic and E. Seneta [Math. Z. 134, 91-106 (1973; Zbl 0264.40003)]. The paper under review proves that \((c_n)\) is a \({\mathcal O}\)-regularly varying sequence if and only if its index function \(k_c\) is a \({\mathcal O}\)-regularly varying function. Reviewer: Stevan Pilipović (Novi Sad) Cited in 5 Documents MSC: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 40A30 Convergence and divergence of series and sequences of functions 40D99 Direct theorems on summability Keywords:\({\mathcal O}\)-regularly varying functions and sequences Citations:Zbl 0264.40003 PDFBibTeX XMLCite \textit{D. Đurčić} and \textit{V. Božin}, Publ. Inst. Math., Nouv. Sér. 62(76), 46--52 (1997; Zbl 0946.26002)