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Open AccessArticle

On Convergence Rates of Some Limits

1
Research Centre for Mathematics, Education, Econometrics and Statistics (MEES), Catholic University Leuven at Campus Brussels, Warmoesberg 26, 1000 Brussels, Belgium
2
Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas, Sangolqui 171103, Ecuador
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 634; https://doi.org/10.3390/math8040634
Received: 9 March 2020 / Revised: 16 April 2020 / Accepted: 17 April 2020 / Published: 21 April 2020
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
In 2019 Seneta has provided a characterization of slowly varying functions L in the Zygmund sense by using the condition, for each y > 0 , x L ( x + y ) L ( x ) 1 0 as x . Very recently, we have extended this result by considering a wider class of functions U related to the following more general condition. For each y > 0 , r ( x ) U ( x + y g ( x ) ) U ( x ) 1 0 as x , for some functions r and g. In this paper, we examine this last result by considering a much more general convergence condition. A wider class related to this new condition is presented. Further, a representation theorem for this wider class is provided. View Full-Text
Keywords: slowly varying; monotony in the Zygmund sense; class Γa(g); self-neglecting function; convergence rates slowly varying; monotony in the Zygmund sense; class Γa(g); self-neglecting function; convergence rates
MDPI and ACS Style

Omey, E.; Cadena, M. On Convergence Rates of Some Limits. Mathematics 2020, 8, 634.

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