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INEQUALITIES FOR THE HILBERT TRANSFORM OF FUNCTIONS WHOSE DERIVATIVES ARE CONVEX

  • Dragomir, S.S. (School of Communications and Informatics Victoria University of Technology)
  • Published : 2002.09.01

Abstract

Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established. Some numerical experiments are performed as well.

Keywords

References

  1. Fourier Analysis and Approximation Theory v.1 P. L. Butzer;R. J. Nessel
  2. Computing v.15 Quadrature formaulas for Cauchy principal value integrals M. M. Chawla;N. Jayarajan https://doi.org/10.1007/BF02260318
  3. Ricerche Mat. v.35 On the convergence of Gauss quadrature rules for the cauchy principal value integrals G. Criscuolo;G. Mastroianni
  4. Numer. Math. v.54 On the unidorm convergence of Gaussian quadrature rules for cauchy principal value integrals G. Criscuolo https://doi.org/10.1007/BF01396323
  5. Methods of Numerical Integration(2nd Ed.) P. J. Davis;P. Rabinowitz
  6. Proc. Sympos. Appl. Math. v.48 Error estimates for a quadrature rule for Cauchy principal value integrals K. Diethelm https://doi.org/10.1090/psapm/048/1314858
  7. Computing v.52 Modified compound quadrature rules for strongly singular integrals K. Diethelm https://doi.org/10.1007/BF02276881
  8. Numer. Math. Peano kernels and bounds for the error constants of Gaussian and related quadrature rules for Cauchy principal value integrals K. Diethelm
  9. J. Comput. Appl. Math v.56 no.3 Uniform convergence to optimal order quadrature rules for Cauchy principal value integrads K. Diethelm https://doi.org/10.1016/0377-0427(94)90086-8
  10. Approx. Theory Appl.(N.S.) v.11 no.4 Asymptotically sharp error bounds for a quadrature rule for Cauchy principal value integrals based on a piecewise linear interpolation K. Diethelm
  11. Inequality Theory and Applications v.1 Some inequalities for the finite Hilbert transform N. M. Dragomir;S. S. Dragomir;P. Farell;Y. J. Cho(Eds.);J. K. Kim(Eds.);S. S. Dragomir(Eds.)
  12. The application of Bullen's inequality for convex functions to the finite Hibert transform S. S. Dragomir
  13. J. Comput. Appl. Math. v.66 A note on Peano costants of Gauss-Konrod quadrature schemes S. Ehrich https://doi.org/10.1016/0377-0427(95)00173-5
  14. Math. Comp. v.33 Gauss type quadrature rules for Cauchy principal value integrals D. Elliott;D.F.Pager https://doi.org/10.2307/2006042
  15. Boundary Value Problems(English translation) F. D. Gakhov
  16. Numer. Math. v.19 Some Gauss type formulae for the evaluation of Cauchy principal value integrals D. B. Hunter https://doi.org/10.1007/BF01404924
  17. Bull. Amer.Math.Soc. v.48 A note on Hilbert's operator K. Kober https://doi.org/10.1090/S0002-9904-1942-07688-9
  18. IMA J. Numer. Anal v.13 Error estimates for generalized compound quadrature formulas P. Kohler https://doi.org/10.1093/imanum/13.3.477
  19. Computing v.55 Asymptotically sharp error estimates for modified compound quadrature formulae for Cauchy principal value integrals P. Kohler
  20. Approx. Theory Appl.(N. S.) v.13 no.3 On the error of quadrature formulae for Cauchy principal value intefrals based on piecewise interpolation P. Kohler
  21. Springer-Verlag Singular Intergral Operators(English translation) S. G. Mikhlin;S. Prossdorf
  22. Computing v.29 The numerical evaluation of one-dimensional Cauchy principal value intergrals G. Monegato https://doi.org/10.1007/BF02246760
  23. J. Inst. Math. Appl. v.26 Error estimates for three methods of evaluating Cauchy principal value integrals B. Noble;S. Beighton https://doi.org/10.1093/imamat/26.4.431
  24. Math. Nachr. v.169 Holder continuous functions functions and the finithe Hilbert trans form S. Okada;D. Elliot https://doi.org/10.1002/mana.19941690116
  25. Corrigendum: Math. Comp. v.45 Gauss-Konrod integration rules Cauchy principal value integrals P. Rabinowitz
  26. BIT no.4 On the convergence of Hunter's method for Cauchy principal value integrels P. Rabinowitz https://doi.org/10.1007/BF01931261
  27. Computing v.48 On the numerical integration of certain singular integrals, Computing H. W. Stolle;R. StrauB https://doi.org/10.1007/BF02310532