Some quadratic integral inequalities of first order

BronisŁaw Florkiewicz; MaŁgorzata Kuchta

Colloquium Mathematicae (1998)

  • Volume: 75, Issue: 1, page 7-18
  • ISSN: 0010-1354

How to cite

top

Florkiewicz, BronisŁaw, and Kuchta, MaŁgorzata. "Some quadratic integral inequalities of first order." Colloquium Mathematicae 75.1 (1998): 7-18. <http://eudml.org/doc/210531>.

@article{Florkiewicz1998,
author = {Florkiewicz, BronisŁaw, Kuchta, MaŁgorzata},
journal = {Colloquium Mathematicae},
keywords = {absolutely continuous function; integral inequality; quadratic integral inequalities; Sturm-Liouville type; Opial type},
language = {eng},
number = {1},
pages = {7-18},
title = {Some quadratic integral inequalities of first order},
url = {http://eudml.org/doc/210531},
volume = {75},
year = {1998},
}

TY - JOUR
AU - Florkiewicz, BronisŁaw
AU - Kuchta, MaŁgorzata
TI - Some quadratic integral inequalities of first order
JO - Colloquium Mathematicae
PY - 1998
VL - 75
IS - 1
SP - 7
EP - 18
LA - eng
KW - absolutely continuous function; integral inequality; quadratic integral inequalities; Sturm-Liouville type; Opial type
UR - http://eudml.org/doc/210531
ER -

References

top
  1. [1] C. D. Ahlbrandt, Variational inequalities, in: Inequalities, W. N. Everitt (ed.), Dekker, New York, 1991, 1-19. 
  2. [2] P. R. Beesack, Integral inequalities of the Wirtinger type, Duke Math. J. 25 (1958), 477-498. Zbl0082.27104
  3. [3] P. R. Beesack, Hardy's inequality and its extensions, Pacific J. Math. 11 (1961), 39-61. Zbl0103.03503
  4. [4] P. R. Beesack, On an integral inequality of Z. Opial, Trans. Amer. Math. Soc. 104 (1962), 470-475. Zbl0122.30102
  5. [5] P. R. Beesack, Integral inequalities involving a function and its derivative, Amer. Math. Monthly 78 (1971), 705-741. Zbl0223.26012
  6. [6] D. C. Benson, Inequalities involving integrals of functions and their derivatives, J. Math. Anal. Appl. 17 (1967), 292-308. Zbl0146.07404
  7. [7] D. W. Boyd, Best constants in inequalities related to Opial's inequality, ibid. 25 (1969), 378-387. Zbl0176.12702
  8. [8] B. Florkiewicz, Some integral inequalities of Hardy type, Colloq. Math. 43 (1980), 321-330. Zbl0473.26007
  9. [9] B. Florkiewicz, On some integral inequalities of Block type, ibid. 55 (1988), 179-189. 
  10. [10] B. Florkiewicz and A. Rybarski, Some integral inequalities of Sturm-Liouville type, ibid. 36 (1976), 127-141. Zbl0354.26007
  11. [11] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1991. 
  12. [12] A. Krzywicki and A. Rybarski, On some integral inequalities involving Chebyshev weight function, Colloq. Math. 18 (1967), 147-150. Zbl0153.38602
  13. [13] M. Kuchta, Some quadratic integral inequalities of Opial type, Ann. Polon. Math. 63 (1996), 103 -113. Zbl0842.26015
  14. [14] M. Morse and W. Leighton, Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252-286. Zbl0015.02701
  15. [15] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer, Dordrecht 1991. Zbl0744.26011
  16. [16] R. Redheffer, Inequalities with three functions, J. Math. Anal. Appl. 16 (1966), 219-242. Zbl0144.30702
  17. [17] W. T. Reid, Sturmian Theory of Ordinary Differential Equations, Springer, New York, 1980. Zbl0459.34001
  18. [18] G. S. Yang, On a certain result of Z. Opial, Proc. Japan Acad. 42 (1966), 78-83. Zbl0151.05202

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.