THE INDEX FUNCTION OPERATOR FOR O-REGULARLY VARYING FUNCTIONS
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Датум
2023
Наслов журнала
Журнал ISSN
Наслов волумена
Издавач
University of Kragujevac, Faculty of Science
Апстракт
The paper examines the functional transformation K of the class ORVφ (see [3]) into the class of positive functions on interval (0,+∞) defined as follows:
(0.1) K(f) = kf ,
where
kf (λ) = limsup
x→+∞
f(λx)
f(x) , λ ∈ (0,+∞),
and f ∈ ORVφ.
Let f ∈ IRVφ or SOφ (see [4]), K be the transformation (0.1) and for any n ∈ N,
Kn(f) = K(K · · · (K | {z }
n
(f)) · · · ), then the function p(s) = limn→+∞ Kn(f)(s), s > 0,
is IRVφ (and continuous) and SOφ, respectively.
Опис
Кључне речи
O-regularly varying function, index function.