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A proof of an Aljančić hypothesis on \({\mathcal O}\)-regularly varying sequences. (English) Zbl 0946.26002

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.

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

Citations:

Zbl 0264.40003
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