Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A generalization of slowly varying functions


Authors: D. Drasin and E. Seneta
Journal: Proc. Amer. Math. Soc. 96 (1986), 470-472
MSC: Primary 26A12
DOI: https://doi.org/10.1090/S0002-9939-1986-0822442-5
MathSciNet review: 822442
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This note establishes that if the main part of the definition of a slowly varying function is relaxed to the requirement that lim $ {\sup _{x \to \infty }}\psi (\lambda x)/\psi (x) < \beta < \infty $ for each $ \lambda > 0$, then $ \psi (x) = L(x)\theta (x)$, where $ L$ is slowly varying and $ \theta $ is bounded. This is done by obtaining a representation for the function $ \psi $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A12

Retrieve articles in all journals with MSC: 26A12


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0822442-5
Keywords: Slowly varying function, uniform convergence, $ R - O$ varying, representation
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society