The weak asymptotic equivalence and the generalized inverse

Djurcic, Dragan; Nikolić, Rale M.; Torgašev, Aleksandar

doi:10.1007/s10986-010-9069-1

Cited by 9 publications

(18 citation statements)

References 14 publications

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“…Thanks to the connection between the γ index, the upper Matuszewska index and the almost monotonicity properties, it is possible to ensure that (9) and (10) are valid under some standard assumptions.…”

Section: Proof the Largest Convex Minorant Of H Can Be Represented Bymentioning

confidence: 99%

Indices of O-regular variation for weight functions and weight sequences

Jiménez-Garrido

Sanz

Schindl

2019

RACSAM

140

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A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure, obtained from a weight function or sequence subject to standard conditions entailing desirable properties (algebraic closure, stability under operators, interpolation, etc.) for the corresponding spaces. The aim of this paper is to stress or reveal the true nature of these diverse conditions imposed on weights, appearing in a scattered and disconnected way in the literature: they turn out to fall into the framework of O-regular variation, and many of them are equivalent formulations of one and the same feature. Moreover, we study several indices of regularity/growth for both functions and sequences, which allow for the rephrasing of qualitative properties in terms of quantitative statements.

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Section: Proof the Largest Convex Minorant Of H Can Be Represented Bymentioning

confidence: 99%

Indices of O-regular variation for weight functions and weight sequences

Jiménez-Garrido

Sanz

Schindl

2019

RACSAM

140

View full text Add to dashboard Cite

show abstract

“…Its generalized inverse (see [1,15]) (x [t] ) ← , t x 1 , belongs to the class ORV f (see [11]). But, since (x [t] ) ← is strongly asymptotically equivalent to δ x (t) for t → ∞ [12], one has δ x ∈ ORV f .…”

Section: Resultsmentioning

confidence: 99%

“…But, according to [16] δ x is strongly asymptotically equivalent to (x [t] ) ← (for t → ∞), so that (x [t] ) ← ∈ ORV f . By a result from [11], x [t] belongs to the class PI * f . Therefore, x ∈ PI * s .…”

Section: Resultsmentioning

confidence: 99%

“…One of main aims of this note is to show that it is possible. Even more: the first coordinate also can be replaced by a wider class PI * s of sequences considered in [3] and [11]. We also show a result of the generalized Galambos-Bojanić-Seneta type; such theorems describe the asymptotic behavior of a sequence by the asymptotic behavior of a corresponding real function.…”

Section: Introductionmentioning

confidence: 86%

“…A sequence x = (x n ) n∈N of positive real numbers is said to belong to the class PI * s [3,11] if there is λ 0 1 such that for each λ > λ 0 it holds…”

Section: Regular Variationmentioning

confidence: 99%

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