Some quadratic integral inequalities of first order

• Autorzy: BronisŁaw Florkiewicz , MaŁgorzata Kuchta
• Języki publikacji: EN

Słowa kluczowe

EN

absolutely continuous function; integral inequality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 75
• Numer: 1
• Strony: 7-18

Daty

wydano

1998

otrzymano

1996-04-23

poprawiono

1997-02-28

Twórcy

autor

BronisŁaw Florkiewicz

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

autor

MaŁgorzata Kuchta

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

Bibliografia

• [1] C. D. Ahlbrandt, Variational inequalities, in: Inequalities, W. N. Everitt (ed.), Dekker, New York, 1991, 1-19.
• [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.