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Open AccessArticle

On Convergence Rates of Some Limits

Research Centre for Mathematics, Education, Econometrics and Statistics (MEES), Catholic University Leuven at Campus Brussels, Warmoesberg 26, 1000 Brussels, Belgium
Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas, Sangolqui 171103, Ecuador
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 634;
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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