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A Theorem of Galambos-Bojanić-Seneta Type

Authors
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Abstract and Applied Analysis
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Disciplines
  • Mathematics

Abstract

In the theorems of Galambos-Bojanić-Seneta's type, the asymptotic behavior of the functions 𝑐 [ 𝑥 ] , 𝑥 ≥ 1 , for 𝑥 → + ∞ , is investigated by the asymptotic behavior of the given sequence of positive numbers ( 𝑐 𝑛 ) , as 𝑛 → + ∞ 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 l i m 𝑛 → ∞   𝑐 [ 𝜆 𝑛 ] / 𝑐 𝑛 > 1 , for 𝜆 > 1 .

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