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Inequalities for sourcewise representable functions and their applications

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Abstract

We prove a discrete and an integral version of an inequality for sourcewise representable functions and use them to derive the Wirtinger inequality and its generalizations.

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References

  1. G. Hardy, D. Littlewood, and G. Pólya,Inequalities, Cambridge Univ. Press, Cambridge (1952).

    Google Scholar 

  2. V. A. Steklov,Fundamental Problems of Mathematical Physics. P. I, II [in Russian], Russian Academy of Sciences, Petersburg, (1922–1923).

    Google Scholar 

  3. W. Blaschke,Kreis und Kugel, W. de Gruyter, Berlin (1956).

    Google Scholar 

  4. E. K. Godunova and V. I. Levin, “On some integral inequalities containing derivatives,”Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], No. 12, 20–24 (1969).

    Google Scholar 

  5. S. L. Sobolev,Some Applications of Functional Analysis to Mathematical Physics [in Russian], Siberian Division of the Russian Academy of Sciences, Novosibirsk (1962).

    Google Scholar 

  6. S. M. Nikol'skii,Approximation to Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  7. A. P. Buslaev and V. M. Tikhomirov, “Some problems of nonlinear analysis and approximation theory,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],283, No. 1, 13–18 (1985).

    MathSciNet  Google Scholar 

  8. A. P. Buslaev and V. M. Tikhomirov, “Spectra of nonlinear differential equations and sections of Sobolev classes,”Mat. Sb. [Math. USSR-Sb.],181, No. 12, 1587–1606 (1990).

    Google Scholar 

  9. Nguen T'en Nam, “Spectrum of nonlinear integral equations and sections of function classes,”Mat. Zametki [Math. Notes],53, No. 4, 101–110 (1993).

    MathSciNet  Google Scholar 

  10. V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin,Optimal Control [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  11. R. Kh. Sadikova, “Inequalities for sourcewise representable functions,”Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], No. 11, 62–64 (1979).

    MATH  MathSciNet  Google Scholar 

  12. R. Kh. Sadikova, “Inequalities with derivatives,”Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], Dep., No. 2632-84 (1984).

  13. R. Kh. Sadikova, “Inequalities for partial derivatives,”Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], Dep., No. 3397-89 (1989).

  14. R. Kh. Sadikova,A general class of inequalities with exact constants [in Russian], Kandidat thesis in the physico-mathematical sciences, Peoples Friendship University, Moscow (1990).

    Google Scholar 

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Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 564–576, October, 1997.

Translated by M. A. Shishkova

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Sadikova, R.K. Inequalities for sourcewise representable functions and their applications. Math Notes 62, 469–479 (1997). https://doi.org/10.1007/BF02358980

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