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ArticleOriginal scientific text

Title

Some quadratic integral inequalities of first order

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  2. Institute of Mathematics Technical, University of Wrocław, Wybrzeże Wyspiańskiego, 27 50-370 Wrocław, Poland

Keywords

ENG
absolutely continuous function, integral inequality

Bibliography

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  2. P. R. Beesack, Integral inequalities of the Wirtinger type, Duke Math. J. 25 (1958), 477-498.
  3. P. R. Beesack, Hardy's inequality and its extensions, Pacific J. Math. 11 (1961), 39-61.
  4. P. R. Beesack, On an integral inequality of Z. Opial, Trans. Amer. Math. Soc. 104 (1962), 470-475.
  5. P. R. Beesack, Integral inequalities involving a function and its derivative, Amer. Math. Monthly 78 (1971), 705-741.
  6. D. C. Benson, Inequalities involving integrals of functions and their derivatives, J. Math. Anal. Appl. 17 (1967), 292-308.
  7. D. W. Boyd, Best constants in inequalities related to Opial's inequality, ibid. 25 (1969), 378-387.
  8. B. Florkiewicz, Some integral inequalities of Hardy type, Colloq. Math. 43 (1980), 321-330.
  9. B. Florkiewicz, On some integral inequalities of Block type, ibid. 55 (1988), 179-189.
  10. B. Florkiewicz and A. Rybarski, Some integral inequalities of Sturm-Liouville type, ibid. 36 (1976), 127-141.
  11. G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1991.
  12. A. Krzywicki and A. Rybarski, On some integral inequalities involving Chebyshev weight function, Colloq. Math. 18 (1967), 147-150.
  13. M. Kuchta, Some quadratic integral inequalities of Opial type, Ann. Polon. Math. 63 (1996), 103 -113.
  14. M. Morse and W. Leighton, Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252-286.
  15. D. S. Mitrinović, J. E. Pe\v carić and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer, Dordrecht 1991.
  16. R. Redheffer, Inequalities with three functions, J. Math. Anal. Appl. 16 (1966), 219-242.
  17. W. T. Reid, Sturmian Theory of Ordinary Differential Equations, Springer, New York, 1980.
  18. G. S. Yang, On a certain result of Z. Opial, Proc. Japan Acad. 42 (1966), 78-83.
Colloquium Mathematicum
1998/75/1
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Pages:
7-18
Main language of publication
English
Received
1996-04-23
Accepted
1997-02-28
Published
1998
Exact and natural sciences