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On an elementary inclusion problem and generalized weighted quasi-arithmetic means

Tom 99 / 2013

Zoltán Daróczy, Zsolt Páles Banach Center Publications 99 (2013), 45-54 MSC: 39B22. DOI: 10.4064/bc99-0-4

Streszczenie

The aim of this note is to characterize the real coefficients $p_1,\dots,p_n$ and $q_1,\dots,q_k$ so that \[\def\conv{\mathop{\rm conv}} \sum_{i=1}^n p_ix_i+\sum_{j=1}^k q_jy_j\in\conv\{x_1,\dots,x_n\} \] be valid whenever the vectors $x_1,\dots,x_n$, $y_1,\dots,y_k$ satisfy \[\def\conv{\mathop{\rm conv}} \{y_1,\dots,y_k\}\subseteq\conv\{x_1,\dots,x_n\}. \] Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.

Autorzy

  • Zoltán DaróczyInstitute of Mathematics
    University of Debrecen
    H-4010 Debrecen
    Pf. 12
    Hungary
    e-mail
  • Zsolt PálesInstitute of Mathematics
    University of Debrecen
    H-4010 Debrecen
    Pf. 12
    Hungary
    e-mail

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