The Bushell-Okrasiński inequality

• Autorzy: Płociniczak Łukasz

Identyfikatory

DOI

10.14708/ma.v50i1.7130

Warianty tytułu

PL

Nierówność Bushella-Okrasińskiego

• Języki publikacji: PL

Abstrakty

PL

W niniejszej pracy omawiamy nierówność Bushella-Okrasiego: jej historię, motywacje za nią stojące oraz kilka uogólnień. Ta nierówność pierwotnie pojawiła się w badaniach nieliniowych równań Volterry, ale bardzo szybko zdobyła zainteresowanie wielu matematyków. Podstawowy wynik został szybko uogólniony i rozszerzony w różnych kierunkach. Między innymi inni autorzy wzmocnili główną tezę, uogólnili jądro oraz nieliniowość, wyznaczyli optymalną stałą multiplikatywną, znaleźli warunki, przy których występuje równość oraz sformułowali liczne warianty ważne dla całek innych niż Lebesgue’a. Dokonujemy przeglądu wszystkich tych aspektów.

EN

We present an expository account of the Bushell-Okrasiński inequality, the motivation behind it, its history, and several generalizations. This inequality originally appeared in studies of nonlinear Volterra equations but very soon gained interest of its own. The basic result has quickly been generalized and extended in different directions strengthening the assertion, generalizing the kernel and nonlinearity, providing the optimal prefactor, finding conditions under which it becomes an equality, and formulating variations valid for other than Lebesgue integrals. We review all of these aspects.

Słowa kluczowe

PL

nierówność Bushella-Okrasińskiego; odwrotna nierówność Jensena; nieliniowe równania Volterry

EN

Bushell-Okrasiński inequality; reversed Jensen inequality; nonlinear Volterra equations

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2022
• Tom: Vol. 50, no. 1
• Strony: 3--22
• Opis fizyczny: Bibliogr. 39 poz.

Twórcy

autor

Płociniczak Łukasz

• Wrocław University of Science and Technology Faculty of Pure and Applied Mathematics Hugo Steinhaus Center Wybrzeże Wyspiańskiego 27, 50–370 Wrocław

• https://orcid.org/0000-0003-0005-4845

Bibliografia

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Uwagi

PL

Opracowane ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)