Skip to main content
SpringerLink
Log in

The Centroid Method in Inequalities

  • Chapter
Classical and New Inequalities in Analysis

Part of the book series: Mathematics and Its Applications () ((MAEE,volume 61))

Abstract

The concept of the centroid, introduced most likely by Archimedes, can be applied in solving various Mathematical problems. We mention, for example, the papers of K. F. Gauss [1] and L. Fejér [2]. Here we shall give a chronological account of the use of the centroid in developing inequalities, pointing to some priorities which are neglected in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 709.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 899.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 899.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. GAUSS, K. F., Werke, t. 3 (1876), p. 112; t. 8 (1900), p. 32.

    Google Scholar 

  2. FEJER, L., Uber die Wurzel von kleinstem absoluten Betrage einer algebraischen Gleichung, Math. Annalen 65 (1908), 413–423.

    Google Scholar 

  3. BALK, M. B., Geometric applications of the concept of centre of gravity ( Russian ), Moskva, 1959, 230 pp.

    Google Scholar 

  4. GROLOUS, J., Un théorème sur les fonctions, L’Institut. J.urnal Universel des Sciences et des Sociétés Savantes en France. Première section, Sciences Mathématiques (2) 3 (1875), 401.

    Google Scholar 

  5. LOB, H., A formula in inequalities, Math. Gaz. 12 (1924), 15–17.

    Google Scholar 

  6. IYENGAR, M. N. NARASIMHA, A graphical treatment of certain inequalities, Math. Student 1 (1933), 89–93.

    Google Scholar 

  7. TOMIC, M. Gauss’ theorem on the centroid and its applications (Serbian), Bull. Soc. M.th. Phys. Serbie (1) 1 (1949), 31–40.

    Google Scholar 

  8. LOWAN, A. N., Note on an elementary method for generating inequalities, Scripta Math. 21 (1955), 218–220.

    Google Scholar 

  9. BARTON, A., An inequality, Math. Gaz. 52 (1968), 383–384.

    Article  Google Scholar 

  10. Cours de M. Hermite,professé pendant le 2e semestre 1881–82. Redigé par M. ANDOYER. Second tirage revue par M. HERMITE. Paris 1883, 48–49.

    Google Scholar 

  11. GHEORGHIU, S. A., Note sur une inégalité de Cauchy, Bull. Math. Soc. Roumainie Sci. 35 (1933), 117–119.

    Google Scholar 

  12. HARDY, G. H., J. E. LITTLEWOOD, G. PÔLYA, Inequalities, Cambridge, 1934.

    Google Scholar 

  13. POLYA, G. and G. SZEGO, Aufgaben und Lehrsätze aus der Analysis, Vol. I. Berlin, 1925, p. 57 and pp. 213–214.

    Google Scholar 

  14. KANTOROVIC, L. V., Functional analysis and applied mathematics (Russian). Uspehi Mat. Nauk (N. S.) 3 No. 6 (28) (1948), 89–185 (in particular, pp. 142–144) (also tranlated from Russian into English by C. D. BENSTER, Nat. Bur. Standards Rep. No. 1509 (1952) 202 pp. - in particular, pp. 106–109).

    Google Scholar 

  15. GREUB, W. and W. RHEINBOLDT, On a generalization of an inequality of L. V. Kantorovich, Proc. Amer. Math. Soc. 10 (1959), 407–415.

    Article  MathSciNet  MATH  Google Scholar 

  16. SPECHT, W., Zur Theorie der elementaren Mittel, Math. Z. 74 (1960), 91–98.

    Google Scholar 

  17. CARGO, G. T. and O. SHISHA, Bounds on ratios of means, J. Res. Nat. Bur. Standards Sect. B, 66B (1962), 169–170.

    Google Scholar 

  18. DIAZ, J. B., A. J. GOLDMAN and F. T. METCALF, Equivalence of certain inequalities complementary to those of Cauchy, Schwarz and Hölder, J. Res. Nat. Bur. Standards Sect. B, 68B (1964), 147–149.

    Article  MathSciNet  MATH  Google Scholar 

  19. FRUCHT, R., On some inequalities (Spanish), Math. Notae 3 (1943), 41–46.

    Google Scholar 

  20. SALEME, E. M., Problem 21, Math. Notae 2 (1942), 197–199.

    Google Scholar 

  21. KESTELMAN, H., A centroidal inequality,Math. Gaz. 46 (1962), 140141.

    Google Scholar 

  22. MITRINOVIC, D. S. and P. M. VASIC, The centroid method in inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Math. Fiz. No. 498–541 (1975), 3–16.

    MathSciNet  Google Scholar 

  23. GHEORGHITZA, St. I., On a method for generating inequalities, J. Math. Phys. Sci. Madras 5 (1971), 232–238.

    MathSciNet  Google Scholar 

  24. LAH, P. and M. RIBARIC, Converse of Jensen’s inequality for convex functions, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 412–460 (1973), 201–205.

    MathSciNet  Google Scholar 

  25. VASIC, P. M. and J. E. PECARIC, On Jensen inequality, Univ. Beograd. Publ. Electrotehn. Fak. Ser. Mat. Fiz. No. 634–677 (1979), 50–54.

    MathSciNet  Google Scholar 

  26. BEESACK, P. R., On inequalities complementary to Jensen’s, Canad. J. Math. 35 (1983), 324–338.

    MathSciNet  MATH  Google Scholar 

  27. PECARIC, J. E. and P. R BEESACK, On Knopp’s inequality for convex functions, Canad. Math. Bull. 30 (1987), 267–272.

    Article  MATH  Google Scholar 

  28. REDHEFFER, R., From center of gravity to Bernstein’s theorem, Amer. Math. Monthly 90 (1983), 130–131.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Belgrade, Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Zagreb, Croatia

    J. E. Pečarić

  3. Department of Mathematics, Iowa State University of Science and Technology, Ames, Iowa, USA

    A. M. Fink

Authors
  1. D. S. Mitrinović
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. E. Pečarić
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. M. Fink
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1993). The Centroid Method in Inequalities. In: Classical and New Inequalities in Analysis. Mathematics and Its Applications (East European Series), vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1043-5_27

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1043-5_27

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4225-5

  • Online ISBN: 978-94-017-1043-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation