Schur convexity of Gnan mean for two variables

V. Lokesha, K. M. Nagaraja, Naveen Kumar B. and Y.-D. Wu
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 17, 2011, Number 4, Pages 37—41
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Authors and affiliations

V. Lokesha
Department of Mathematics, Acharya institute of Technology
Bangalore-90, India

K. M. Nagaraja
Department of Mathematics, J.S.S.I. Technology
Bangalore, India

Naveen Kumar B.
Department Of Mathematics, R.N.S. Institute of Technology
Bangalore-61, India

Y.-D. Wu
Xinchang High School
Xinchang City, Zhejiang Province 312500, P. R. China

Abstract

In this paper, the convexity and Schur convexity of the Gnan mean and its dual form in two variables are discussed.

Keywords

  • Mean
  • Monotonicity
  • Inequality
  • Convexity

AMS Classification

  • 26D15

References

  1. Bullen, P. S. Handbook of Means and Their Inequalities, Kluwer Acad. Publ., Dordrecht, 2003.
  2. Lokesha, V., Zh.-H. Zhang, K. M. Nagaraja, Gnan Mean for two variables, Far East Journal of Mathematics, Vol. 31, 2008, No. 2, 263–272.
  3. Lokesha, V., Zh.-H. Zhang, Y.-D. Wu, Two weighted product type means and its monotonicities, RGMIA Research Report Collection, Vol. 8, 2005, No. 1, Article 17. http://rgmia.vu.edu.au/v8n1.html
  4. Webster, R. Convexity. Oxford University Press, Oxford, New York, Tokyo, 1994.
  5. Zhang, Zh.-H., Y.-D. Wu, The generalized Heron mean and its dual form. Appl. Math. ENotes, Vol. 5, 2005, 16–23. http://www.math.nthu.edu.tw/~amen/
  6. Xiao, Zh.-G., Zh.-H. Zhang. The Inequalities G 6 L 6 I 6 A in n Variables, J. Ineq. Pure & Appl. Math., Vol. 4, 2003, No. 2, Article 39. http://jipam.vu.edu.au/v4n2/110_02.pdf
  7. Xiao, Zh.-G., Zh.-H. Zhang, V. Lokesha. The weighted Heron mean of several positive numbers, RGMIA Research Report Collection, Vol. 8, 2005, No. 3, Article 6. http://rgmia.vu.edu.au/v8n3.html
  8. Xiao, Zh.-G., V. Lokesha, Zh.-H. Zhang. The weighted Heron dual mean of several positive numbers, RGMIA Research Report Collection, Vol. 8, 2005, No. 4, Article 19. http://rgmia.vu.edu.au/v8n4.html

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Cite this paper

APA

Lokesha, V., Nagaraja, K. M., Naveen Kumar B., Wu, Y.-D. Schur convexity of Gnan mean for two variables, Notes on Number Theory and Discrete Mathematics, 17(4), 37-41.

Chicago

Lokesha, V., K. M. Nagaraja, Naveen Kumar B., and Y.-D. Wu. “Schur Convexity of Gnan Mean for Two Variables.” Notes on Number Theory and Discrete Mathematics 17, no. 4 (2011): 37-41.

MLA

Lokesha, V., K. M. Nagaraja, Naveen Kumar B., and Y.-D. Wu. “Schur Convexity of Gnan Mean for Two Variables.” Notes on Number Theory and Discrete Mathematics 17.4 (2011): 37-41. Print.

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