[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2002.39.5.709

INEQUALITIES FOR THE HILBERT TRANSFORM OF FUNCTIONS WHOSE DERIVATIVES ARE CONVEX

Dragomir, S.S. (School of Communications and Informatics Victoria University of Technology)

Publication Information

Journal of the Korean Mathematical Society / v.39, no.5, 2002 , pp. 709-729 More about this Journal

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

finite Hilbert transform; Hermite-Hadamard inequality;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	Holder continuous functions functions and the finithe Hilbert trans form / [ S. Okada;D. Elliot ] / Math. Nachr. DOI
2	Gauss-Konrod integration rules Cauchy principal value integrals / [ P. Rabinowitz ] / Corrigendum: Math. Comp.
3	A note on Hilbert's operator / [ K. Kober ] / Bull. Amer.Math.Soc. DOI
4	On the error of quadrature formulae for Cauchy principal value intefrals based on piecewise interpolation / [ P. Kohler ] / Approx. Theory Appl.(N. S.)
5	Error estimates for three methods of evaluating Cauchy principal value integrals / [ B. Noble;S. Beighton ] / J. Inst. Math. Appl. DOI
6	Asymptotically sharp error bounds for a quadrature rule for Cauchy principal value integrals based on a piecewise linear interpolation / [ K. Diethelm ] / Approx. Theory Appl.(N.S.)
7	/ [ P. J. Davis;P. Rabinowitz ] / Methods of Numerical Integration(2nd Ed.)
8	Some Gauss type formulae for the evaluation of Cauchy principal value integrals / [ D. B. Hunter ] / Numer. Math. DOI
9	A note on Peano costants of Gauss-Konrod quadrature schemes / [ S. Ehrich ] / J. Comput. Appl. Math. DOI ScienceOn
10	Error estimates for generalized compound quadrature formulas / [ P. Kohler ] / IMA J. Numer. Anal DOI ScienceOn
11	Asymptotically sharp error estimates for modified compound quadrature formulae for Cauchy principal value integrals / [ P. Kohler ] / Computing
12	Uniform convergence to optimal order quadrature rules for Cauchy principal value integrads / [ K. Diethelm ] / J. Comput. Appl. Math DOI ScienceOn
13	Error estimates for a quadrature rule for Cauchy principal value integrals / [ K. Diethelm ] / Proc. Sympos. Appl. Math. DOI
14	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.) ] / Inequality Theory and Applications
15	The numerical evaluation of one-dimensional Cauchy principal value intergrals / [ G. Monegato ] / Computing DOI
16	On the unidorm convergence of Gaussian quadrature rules for cauchy principal value integrals / [ G. Criscuolo ] / Numer. Math. DOI
17	/ [ F. D. Gakhov ] / Boundary Value Problems(English translation)
18	On the convergence of Hunter's method for Cauchy principal value integrels / [ P. Rabinowitz ] / BIT DOI
19	Gauss type quadrature rules for Cauchy principal value integrals / [ D. Elliott;D.F.Pager ] / Math. Comp. DOI ScienceOn
20	Quadrature formaulas for Cauchy principal value integrals / [ M. M. Chawla;N. Jayarajan ] / Computing DOI ScienceOn
21	/ [ P. L. Butzer;R. J. Nessel ] / Fourier Analysis and Approximation Theory
22	On the numerical integration of certain singular integrals, Computing / [ H. W. Stolle;R. StrauB ] / Computing DOI
23	/ [ S. S. Dragomir ] / The application of Bullen's inequality for convex functions to the finite Hibert transform
24	On the convergence of Gauss quadrature rules for the cauchy principal value integrals / [ G. Criscuolo;G. Mastroianni ] / Ricerche Mat.
25	Peano kernels and bounds for the error constants of Gaussian and related quadrature rules for Cauchy principal value integrals / [ K. Diethelm ] / Numer. Math.
26	Modified compound quadrature rules for strongly singular integrals / [ K. Diethelm ] / Computing DOI ScienceOn
27	Singular Intergral Operators(English translation) / [ S. G. Mikhlin;S. Prossdorf ] / Springer-Verlag