References
Paul R. Beesack,On an integral inequality of Z. Opial, Trans. Amer. Math. Soc.104 (1962), 470–475.
David W. Boyd,Best constants in a class of integral inequalities, Pacific J. Math.30 (1969), 367–383.
David W. Boyd,Inequalities for positive integral operators, Pacific J. Math.38 (1971), 9–24.
D. W. Boyd and J. S. W. Wong,An extension of Opial's inequality, J. Math. Anal. Appl.19 (1967), 100–102.
K. M. Das and P. R. Beesack,Extensions of Opial's inequality, Pacific J. Math.26 (1968), 215–232.
G. H. Hardy, J. E. Littlewood and G. Pólya,Inequalities, 2nd ed., Cambridge, 1952.
L. K. Hua,On an inequality of Opial, Scientia Sinica14 (1965), 789–790.
N. Levinson,On an inequality of Opial and Beesack, Proc. Amer. Math. Soc.,15 (1964), 565–566.
C. L. Mallows,An even simpler proof of Opial's inequality. Proc. Amer. Math. Soc.16 (1965), 173.
P. M. Maroni,Sur l'inégalité d'Opial-Beesack, C. R. Acad. Sci. ParisA 264 (1967), 62–64.
C. Olech,A simple proof of a certain results of Z. Opial, Ann. Polon. Math.8 (1960), 61–63.
Z. Opial,Sur une inégalité, Ann. Polon. Math.8 (1960), 29–32.
R. N. Pederson,On an inequality of Opial, Beesack and Levinson, Proc. Amer. Math. Soc.16 (1965), 174.
Daniel T. Shum,On a class of new inequalities, Trans. Amer. Math. Soc.204 (1975), 299–341.
G. S. Yang,On a certain results of Z. Opial, Proc. Japan Acad.42 (1966), 78–83.
Author information
Authors and Affiliations
Additional information
In memory of Zeev Nehari
Rights and permissions
About this article
Cite this article
Beesack, P.R. Elementary proofs of some Opial-type integral inequalities. J. Anal. Math. 36, 1–14 (1979). https://doi.org/10.1007/BF02798763
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02798763