On Convergence Rates of Some Limits

Edward Omey and Meitner Cadena
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Edward Omey: Research Centre for Mathematics, Education, Econometrics and Statistics (MEES), Catholic University Leuven at Campus Brussels, Warmoesberg 26, 1000 Brussels, Belgium
Meitner Cadena: Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas, Sangolqui 171103, Ecuador

Mathematics, 2020, vol. 8, issue 4, 1-17

Abstract: 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.

Keywords: slowly varying; monotony in the Zygmund sense; class ? a ( g ); self-neglecting function; convergence rates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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