New Chebyshev type inequalities for sequences of real numbers

Authors

  • S. S. Dragomir School of Computer Science & Mathematics Victoria University, Melbourne, Australia

DOI:

https://doi.org/10.33993/jnaat331-759

Keywords:

Chebyshev inequality
Abstract views: 209

Abstract

Some new inequalities of Chebyshev type for sequences of real numbers are pointed out.

Downloads

Download data is not yet available.

References

Chebyshev, P. L. (1882), O približennyh vyraženijah odnih integralov čerez drugie, Soobšćenija i protokoly zasedaniĭ Matemmatičeskogo občestva pri Imperatorskom Har'kovskom Universitete, No. 2, pp. 93-98; Polnoe sobranie sočineniĭ P. L. Chebysheva. Moskva-Leningrad, 1948a, pp. 128-131.

Chebyshev, P. L. (1883), Ob odnom rjade, dostavljajušćem predel'nye veličiny integralov pri razloženii podintegral'noĭ funkcii na množeteli, Priloženi k 57 tomu Zapisok Imp. Akad. Nauk, No. 4; Polnoe sobranie sočineniĭ P. L. Chebysheva. Moskva-Leningrad, 1948b, pp. 157-169.

Hardy, G. H., Littlewood, J.E. and Pólya, G., Inequalities, 1st Ed. and 2nd Ed., Cambridge University Press, Cambridge, England, 1934, 1952.

Biernacki, M., Sur une inégalité entre les intégrales due à Tchebyscheff, Ann. Univ. Mariae Curie-Sklodowska, A5, pp. 23-29, 1951.

Sonin, N. Ja., O nekotoryh neravenstvah, ostnosjaščihsja k opredelennym integralam, Zap. Imp. Akad. Nauk po Fiziko-Matem. Otd., 6, pp. 1-54, 1898.

Mitrinović D. S., Pečarić J. E and Fink A. M., Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, 1993. DOI: https://doi.org/10.1007/978-94-017-1043-5

Korkine, A. N., Sur une théorème de M. Tchebychef, C. R. Acad. Sci. Paris, 96, pp. 326-327, 1883.

Dragomir S. S., A survey on Chebyshev and Grüss type discrete inequalities, in preparation.

Mitrinović D. S. and Pečarić, J. E., On an identity of D.Z. Djoković, Prilozi Mak. Akad. Nauk. Umj. (Skopje), 12(1), pp. 21-22, 1991.

Dragomir, S. S. and Pečarić, J. E., Refinements of some inequalities for isotonic linear functionals, Rev. Anal. Numér. Théor. Approx., 18 (1), pp. 61-65, 1989, http://ictp.acad.ro/jnaat/journal/article/view/1989-vol18-no1-art7

Dragomir, S. S., On some improvements of Chebyshev's inequality for sequences and integrals, Studia Univ. Babeş-Bolyai, Mathematica, XXXV (4), pp. 35-40, 1990.

Pečarić, J. E. and Dragomir, S. S., Some remarks on Chebyshev's inequality, Rev. Anal. Numér. Théor. Approx., 19 (1), pp. 58-65, 1990, http://ictp.acad.ro/jnaat/journal/article/view/1990-vol19-no1-art10

Downloads

Published

2004-02-01

How to Cite

Dragomir, S. S. (2004). New Chebyshev type inequalities for sequences of real numbers. Rev. Anal. Numér. Théor. Approx., 33(1), 61–66. https://doi.org/10.33993/jnaat331-759

Issue

Vol. 33 No. 1 (2004)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.