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Mat. Zametki, 2001, Volume 70, Issue 5, Pages 780–786 (Mi mz789)  

This article is cited in 2 scientific papers (total in 2 papers)

A Criterion for Contiguity of Quasiconcave Functions

V. I. Ovchinnikova, A. S. Titenkovb

a Voronezh State University
b Kursk State University

Abstract: Quasiconcave functions $\rho _0$ and $\rho _1$ belong to the same scale if there exist quasiconcave functions $\psi _0$ and $\psi _1$ and numbers $0<\theta _0<1$, $0<\theta _1<1$ such that $\rho _0=\psi _0^{1-\theta _0}\psi _1^{\theta _0}$ and $\rho _1=\psi _0^{1-\theta _1}\psi _1^{\theta _1}$. We establish a criterion for such functions to belong to the same scale up to equivalence. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences.

DOI: https://doi.org/10.4213/mzm789

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English version:
Mathematical Notes, 2001, 70:5, 708–713

Bibliographic databases:

UDC: 517.982
Received: 03.04.2000

Citation: V. I. Ovchinnikov, A. S. Titenkov, “A Criterion for Contiguity of Quasiconcave Functions”, Mat. Zametki, 70:5 (2001), 780–786; Math. Notes, 70:5 (2001), 708–713

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gogatishvili, A, “Interpolation orbits and optimal Sobolev's embeddings”, Journal of Functional Analysis, 253:1 (2007), 1  crossref  mathscinet  zmath  isi  scopus
    2. V. I. Ovchinnikov, “Interpolation functions and the Lions–Peetre interpolation construction”, Russian Math. Surveys, 69:4 (2014), 681–741  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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