A+ CATEGORY SCIENTIFIC UNIT

Generalized midconvexity

Volume 99 / 2013

Jacek Tabor, Józef Tabor, Krzysztof Misztal Banach Center Publications 99 (2013), 207-215 MSC: Primary 26A51, 39B62; Secondary 26B25. DOI: 10.4064/bc99-0-13

Abstract

There are many types of midconvexities, for example Jensen convexity, $t$-convexity, $(s,t)$-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space $X$.

We show that we can define and study the basic convexity properties in this setting.

Authors

  • Jacek TaborInstitute of Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail
  • Józef TaborInstitute of Mathematics
    University of Rzeszów
    Rejtana 16A
    35-310 Rzeszów, Poland
    e-mail
  • Krzysztof MisztalInstitute of Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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