Integral inequalities associated with inequalities of Opial type

• Autorzy: Florkiewicz, B. , Kuchta, M.
• Języki publikacji: EN

Abstrakty

EN

We derive some new integral inequalities of the form: [...], h [belongs to] H, where I = (alpha, beta), -[infinity is less than or equal alpha < beta is less than or equal infinity], p > 0, H is a wide class of absolutely continuous functions h defined on I and satisfying the limit conditions h(alpha) = 0 or h(beta) = 0, the functions r, s and u are any set of functions related by the appropriate weight functions. To get the desired inequality, at first we derive an integral inequality of Opial type using a uniform method of obtaining integral inequalities with weight functions involving the function and its derivative [2].

Słowa kluczowe

PL

funkcja ciągła bezwzględnie; nierówność całkowa; nierówność Opiala

EN

absolutely continuous function; integral inequality; Opial inequality

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 1
• Strony: 41-45
• Opis fizyczny: Bibliogr. 2 poz.

Twórcy

autor

Florkiewicz, B.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Kuchta, M.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland,

Bibliografia

• [1] B. Florkiewicz, On some integral inequalities of Weyl type, Colloq. Math., 49 (1984) 91-107.
• [2] B. Florkiewicz, On some inequalities of Opial type, J. Inequalities Appl., to be published.