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ON SOME FURTHER WIRTINGER-BEESACK INTEGRAL INEQUALITIES

ON SOME FURTHER WIRTINGER-BEESACK INTEGRAL INEQUALITIES 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON SOME FURTHER WIRTINGER-BEESACK INTEGRAL INEQUALITIES

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References (5)

Publisher
de Gruyter
Copyright
© by Bronislaw Florkiewicz
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1999-0305
Publisher site
See Article on Publisher Site

Abstract

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)

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 1999

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