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: 174

Abstract

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

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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

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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

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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

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