A Theorem of Galambos-Bojanić-Seneta Type

Abstract EN

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 lim¯n→∞ c[λn]/cn>1, for λ>1.