A theorem of Galambos-Bojanić-Seneta type
type: Item
instance of: scholarly article
title: A theorem of Galambos-Bojanić-Seneta type
zbMATH Open document ID: 1168.26300
DOI: 10.1155/2009/360794
author: Dragan Djurčić
author: Aleksandar Torgašev
published in: Abstract and Applied Analysis
publication date: 2009-07-02T00:00:00Z
review text: 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 \(\lambda >1\).
Mathematics Subject Classification ID: 26A12
Mathematics Subject Classification ID: 26A48
zbMATH DE Number: 5574411
zbMATH Keywords: regular variations
zbMATH Keywords: asymptotic behavior
Wikidata QID: Q58646584
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/360794
OpenAlex ID: W2028376723
cites work: Q4726487
cites work: Intermediate Regular and Π Variation
cites work: \(\mathcal O\)-regularly varying functions and strong asymptotic equivalence
cites work: Q3356562
cites work: Sojourns and extremes of a diffusion process on a fixed interval
cites work: Strong asymptotic equivalence and inversion of functions in the class \(K_c\)
cites work: On a generalization of regularly increasing functions
cites work: Q4196856
cites work: Regularly varying functions
cites work: Convergence and the Fourier character of trigonometric transforms with slowly varying convergence moduli
cites work: Structure of Fourier and Fourier-Stieltjes coefficients of series with slowly varying convergence moduli
cites work: Q4827496
cites work: A unified theory of regularly varying sequences
cites work: Regularly Varying Sequences
cites work: Q5633348
cites work: On some classes of functions with regard to their orders of growth
cites work: Rapidly varying sequences and rapid convergence
cites work: A Generalization of Slowly Varying Functions
cites work: Q3369123
cites work: Some properties of rapidly varying sequences
cites work: On the Seneta sequences
cites work: Q5692127
description: scientific article; zbMATH DE number 5574411