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B. Florkiewicz, A. Rybarski (1976)
Some integral inequalities of Sturm-Liouville typeColloquium Mathematicum, 36
B. Florkiewicz (1980)
Some integral inequalities of Hardy typeColloquium Mathematicum, 43
(1996)
u c h t a , Some quadratic integral inequalities of Opial type, Ann
B. Florkiewicz, M. Kuchta (1998)
Some quadratic integral inequalities of first orderColloquium Mathematicum, 75
(1991)
H a r d y
D E M O N S T R A T E MATHEMATICAVol. XXXIINo 31999Bronislaw Florkiewicz, Katarzyna WojteczekON SOME FURTHER WIRTINGER-BEESACKINTEGRAL INEQUALITIES1. IntroductionIn the previous paper [5] the uniform method of obtaining and investigating various types of integral inequalities involving a function and its firstderivative (see [4],[2], [7] and [3]) has been extended to the integral inequalities involving a function andjts second derivative. Some quadratic integralinequalities of the second order of the form(1)\sh2dt<\rh"2dt,IIh e H ,where I = (a,/3),— oo < a < ¡3 < oo, r and s are real functions of thevariable t, H is a class of functions absolutely continuous on I has beenderived.In this paper we derive some new integral inequalities of the form (1).The method we use consists in determining the function s and the auxiliaryfunctions wo, w\ and W2 depending on the given function r and the auxiliary function tp and next using these functions to determine the class H offunctions h for which the inequality (1) holds. The class of functions h forwhich the inequality (1) holds determined in this paper doesn't cover withthe class of functions h obtained in the paper [5].We also derive some new integral inequalities of the form (1)
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 1999
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