A Theorem of Galambos-Bojanić-Seneta Type

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 (𝑐𝑛), as 𝑛→+∞ and vice versa. The main result of this paper is one theorem of such a type for sequences of positive numbers (𝑐𝑛) which satisfy an asymptotic condition of the Karamata type lim𝑛→∞ 𝑐[𝜆𝑛]/𝑐𝑛>1, for 𝜆>1.