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Opial Inequalities Involving Higher-Order Partial Derivatives

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Abstract

In the present paper, we establish some new Opial’s type inequalities involving higher-order partial derivatives. Our results provide new estimates on inequalities of these type.

In Honor of Constantin Carathéodory

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References

  1. Agarwal, R.P.: Sharp Opial-type inequalities involving r-derivatives and their applications. Tohoku Math. J. 47 (4), 567–593 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agarwal, R.P., Lakshmikantham, V.: Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations. World Scientific, Singapore (1993)

    Book  MATH  Google Scholar 

  3. Agarwal, R.P., Pang, P.Y.H.: Opial Inequalities with Applications in Differential and Difference Equations. Kluwer Academic Publishers, Dordrecht (1995)

    Book  MATH  Google Scholar 

  4. Agarwal, R.P., Pang, P.Y.H.: Sharp opial-type inequalities in two variables. Appl. Anal. 56 (3), 227–242 (1996)

    MathSciNet  MATH  Google Scholar 

  5. Agarwal, R.P., Thandapani, E.: On some new integrodifferential inequalities. Anal. sti. Univ. “Al. I. Cuza” din Iasi. 28, 123–126 (1982)

    Google Scholar 

  6. Alzer, H.: An Opial-type inequality involving higher-order derivatives of two functions. Appl. Math. Lett. 10 (4), 123–128 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bainov, D., Simeonov, P.: Integral Inequalities and Applications. Kluwer Academic Publishers, Dordrecht (1992)

    Book  MATH  Google Scholar 

  8. Beesack, P.R.: On an integral inequality of Z. Opial. Trans. Am. Math. Soc. 104, 470–475 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cheung, W.-S.: On Opial-type inequalities in two variables. Aequationes Math. 38, 236–244 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cheung, W.-S.: Some new Opial-type inequalities. Mathematika 37, 136–142 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cheung, W.-S.: Some generalized Opial-type inequalities. J. Math. Anal. Appl. 162, 317–321 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cheung, W.-S.: Opial-type inequalities with m functions in n variables. Mathematika 39, 319–326 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cheung, W.-S., Zhao, D.D., Pečarić, J.E.: Opial-type inequalities for differential operators. Nonlinear Anal. 66 (9), 2028–2039 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Das, K.M.: An inequality similar to Opial’s inequality. Proc. Am. Math. Soc. 22, 258–261 (1969)

    MATH  Google Scholar 

  15. Godunova, E.K, Levin, V.I.: On an inequality of Maroni. Mat. Zametki. 2, 221–224 (1967)

    MathSciNet  Google Scholar 

  16. Hua, L.K.: On an inequality of Opial. Sci. Sin. 14, 789–790 (1965)

    MathSciNet  MATH  Google Scholar 

  17. Karpuz, B., Kaymakcalan, B., Özkan, U.M.: Some multi-dimensional Opial-type inequalities on time scales. J. Math. Inequal. 4 (2), 207–216 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, J.D.: Opial-type integral inequalities involving several higher order derivatives. J. Math. Anal. Appl. 167, 98–100 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mitrinovič, D.S.: Analytic Inequalities. Springer, Berlin, New York (1970)

    Book  MATH  Google Scholar 

  20. Mitrinovič, D.S., Pečarić, J.E., Fink, A.M.: Inequalities Involving Functions and Their Integrals and Derivatives. Kluwer Academic Publishers, Dordrecht (1991)

    Book  MATH  Google Scholar 

  21. Opial, Z.: Sur une inégalité. Ann. Polon. Math. 8, 29–32 (1960)

    MathSciNet  MATH  Google Scholar 

  22. Pachpatte, B.G.: On integral inequalities similar to Opial’s inequality. Demonstratio Math. 22, 21–27 (1989)

    MathSciNet  MATH  Google Scholar 

  23. Yang, G.S.: On a certain result of Z. Opial. Proc. Jpn. Acad. 42, 78–83 (1966)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Research by Chang-Jian Zhao is supported by National Natural Science Foundation of China (11371334). Research by Wing-Sum Cheung is partially supported by a HKU Seed Grant for Basic Research.

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Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, Hangzhou, 310018, P.R. China

    Chang-Jian Zhao

  2. Department of Mathematics, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong

    Wing-Sum Cheung

Authors
  1. Chang-Jian Zhao
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  2. Wing-Sum Cheung
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Corresponding author

Correspondence to Wing-Sum Cheung .

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Editors and Affiliations

  1. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Mathematics, National Technical Unversity of Athens Department of Mathematics, Athens, Greece

    Themistocles M. Rassias

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Zhao, CJ., Cheung, WS. (2016). Opial Inequalities Involving Higher-Order Partial Derivatives. In: Pardalos, P., Rassias, T. (eds) Contributions in Mathematics and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-31317-7_31

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