Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1997, Volume 61, Issue 6, Pages 864–872 (Mi mz1570)  

A general class of inequalities with mixed means

R. Kh. Sadikova

M. V. Lomonosov Moscow State University

Abstract: Suppose $(T,\Sigma,\mu)$ is a space with positive measure, $f\colon\mathbb R\to\mathbb R$ is a strictly monotone continuous function, and $\mathfrak G(T)$ is the set of real $\mu$-measurable functions on $T$. Let $x(\cdot)\in\mathfrak G(T)$ and $(f\circ x)(\cdot)\in L_1(T,\mu)$. Comparison theorems are proved for the means $\mathfrak M_{(T,\mu,f)}(x(\cdot))$ and the mixed means $\mathfrak M_{(T_1,\mu _1,f_1)}(\mathfrak M_{(T_2,\mu_2,f_2)}(x(\cdot)))$ these inequalities imply analogs and generalizations of some classical inequalities, namely those of Hölder, Minkowski, Bellman, Pearson, Godunova and Levin, Steffensen, Marshall and Olkin, and others. These results are a continuation of the author's studies.

DOI: https://doi.org/10.4213/mzm1570

Full text: PDF file (196 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 1997, 61:6, 724–730

Bibliographic databases:

UDC: 517.5
Received: 03.08.1995

Citation: R. Kh. Sadikova, “A general class of inequalities with mixed means”, Mat. Zametki, 61:6 (1997), 864–872; Math. Notes, 61:6 (1997), 724–730

Citation in format AMSBIB
\Bibitem{Sad97}
\by R.~Kh.~Sadikova
\paper A general class of inequalities with mixed means
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 6
\pages 864--872
\mathnet{http://mi.mathnet.ru/mz1570}
\crossref{https://doi.org/10.4213/mzm1570}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629805}
\zmath{https://zbmath.org/?q=an:0914.26010}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 6
\pages 724--730
\crossref{https://doi.org/10.1007/BF02361214}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YE52200026}


Linking options:
  • http://mi.mathnet.ru/eng/mz1570
  • https://doi.org/10.4213/mzm1570
  • http://mi.mathnet.ru/eng/mz/v61/i6/p864

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:230
    Full text:101
    References:38
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021