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Part of the book series: Mathematics and Its Applications ((MAEE,volume 53))

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Abstract

In this Chapter we give a number of different methods for proofs of various integro-differential inequalities, with emphasis on the more elementary methods.

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References

  1. Beesack, P.R., D.S. MitrinoviĆ and P.M. VASIĆ, Integral inequalities, (the manuscript not achieved and not published).

    Google Scholar 

  2. Ewing, G.M., “Calculus of Variations with Applications,” New York, 1969.

    Google Scholar 

  3. Young, L.C., “Calculus of Variations and Optimal Control Theory,” Philadelphia-London-Toronto, 1969.

    Google Scholar 

  4. Hardy, G.H., J.E. Littlewood, and G. PÓlya, “Inequalities,” Cambridge, 1934, 1952.

    Google Scholar 

  5. Florkiewicz, B. and A. Rybarski, Some integral inequalities of Sturm-Liouville type, Colloq. Math. 36 (1976), 127–141.

    MathSciNet  MATH  Google Scholar 

  6. Beesack, P.R., Integral inequalities of Wirtinger type, Duke Math. J. 25 (1958), 477–498.

    Article  MathSciNet  MATH  Google Scholar 

  7. Beesack, P.R.—, Integral inequalities involving a function and its derivative, Amer. Math. Monthly 78 (1971), 705–741.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kamke, E., “Differentialgleichungen, Lösungsmethoden und Lösungen,” 3rd ed., Berlin, 1944.

    Google Scholar 

  9. Reid, W.T., “Ordinary Differential Equations,” New York, 1971.

    Google Scholar 

  10. Everitt, W.N., Spectral theory of the Wirtinger inequality, in Lecture Notes in Mathematics 564, Berlin, 1976, pp. 93–105.

    Article  MathSciNet  Google Scholar 

  11. Krylov, N.M., On some inequalities which will be established in the exposition of the Schwartz-Poincaré-Steklov method and are also encountered in solving many minimization problems, Zapiski Gornago Institute 2 6 (1915), 10–14 (Russian).

    Google Scholar 

  12. Beesack, P.R., Elementary proofs of the extremal properties of the eigenvalues of the Sturm-Liouville equation, Canad. Math. Bull. 3 (1960), 59–77.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hartman, P., “Ordinary Differential Equations,” Baltimore, 1973.

    Google Scholar 

  14. Coddington, P. and N. Levinson, “Theory of Ordinary Differential Equations,” New York, 1955.

    Google Scholar 

  15. Courant, R. and D. Hilbert, “Methods of Mathematical Physics,” Vol. 1, New York, 1953.

    Google Scholar 

  16. Benson, D. C., Inequalities involving integrals of functions and their derivatives, J. Math. Anal. Appl. 17 (1967), 292–308.

    Article  MathSciNet  MATH  Google Scholar 

  17. MitrinoviĆ, D.S., “Analytic Inequalities,” Berlin-Heidelberg-New York, 1970.

    Google Scholar 

  18. Shum, D.T.T., Integral inequalities using Benson’s method, Doctoral dissertation, Carleton University, Ottawa, 1971, 212 pages.

    Google Scholar 

  19. Beesack, P.R., Extensions of Wirtinger’s inequality, Trans. Roy. Soc. Canada 53 3 (1959), 21–30.

    MATH  Google Scholar 

  20. Beesack, P.R. —, Hardy’s inequality and its extensions, Pacific J. Math. 11 (1961), 39–61.

    MathSciNet  MATH  Google Scholar 

  21. Beckenbach, E.F. and R. Bellman, “Inequalities,” Berlin, 1965.

    Google Scholar 

  22. Benson, D.C., Comparison theory for, SIAM J. Math. 21 (1971), 279–286.

    Article  MathSciNet  MATH  Google Scholar 

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© 1991 Springer Science+Business Media Dordrecht

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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1991). Methods of Proofs for Integral Inequalities. In: Inequalities Involving Functions and Their Integrals and Derivatives. Mathematics and Its Applications, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3562-7_17

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  • DOI: https://doi.org/10.1007/978-94-011-3562-7_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5578-9

  • Online ISBN: 978-94-011-3562-7

  • eBook Packages: Springer Book Archive

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