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A theorem of Galambos-Bojanić-Seneta type. (English) Zbl 1168.26300

Summary: In the theorems of Galambos-Bojanić-Seneta’s type, the asymptotic behavior of the functions \(c_{[x]},\, x\geq 1\), for \(x\rightarrow +\infty\), is investigated by the asymptotic behavior of the given sequence of positive numbers \((c_{n})\), as \(n\rightarrow +\infty \) and vice versa. The main result of this paper is one theorem of such a type for sequences of positive numbers \((c_{n})\) which satisfy an asymptotic condition of the Karamata type \(\underline{\lim}_{n \to \infty} c_{[\lambda n]}/c_n > 1\), for \(\lambda >1\).

MSC:

26A12 Rate of growth of functions, orders of infinity, slowly varying functions
26A48 Monotonic functions, generalizations
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