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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## Details

### 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

- Bullen, P. S. Handbook of Means and Their Inequalities, Kluwer Acad. Publ., Dordrecht, 2003.
- 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.
- 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
- Webster, R. Convexity. Oxford University Press, Oxford, New York, Tokyo, 1994.
- 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/
- Xiao, Zh.-G., Zh.-H. Zhang. The Inequalities
*G*≤*L*≤*I*≤*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 - 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
- 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

## Related papers

- Nagaraja, K. M., & Dhanya, P. (2020). Identities on generalized Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, 26 (3), 189-202, doi: 10.7546/nntdm.2020.26.3.189-202.

## Cite this paper

APALokesha, 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.

ChicagoLokesha, 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.

MLALokesha, 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.