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Keywords = monotony in the Zygmund sense

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17 pages, 256 KiB  
Article
On Convergence Rates of Some Limits
by Edward Omey and Meitner Cadena
Mathematics 2020, 8(4), 634; https://doi.org/10.3390/math8040634 - 21 Apr 2020
Cited by 1 | Viewed by 2274
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 , [...] Read more.
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. Full article
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
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