K. M. Nagaraja and P. Siva Kota Reddy
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 1, Pages 22–28
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Authors and affiliations
K. M. Nagaraja
Department of Mathematics, Sri Krishna Institute of Technology
Bangalore-560 090, India
P. Siva Kota Reddy
Department of Mathematics, Acharya Institute of Technology
Bangalore-560 090, India
Abstract
In this paper, using Simpson’s quadrature formula and Jensen inequality for convex function, we obtained some double inequalities among various means.
Keywords
- Inequality
- Simpson’s rule
- Convex function
- Jensen inequality
AMS Classification
- 25D15
References
- Bullen, P. S. Handbook of means and their inequalities, Kluwer Acad. Publ., Dordrecht, 2003.
- Hardy, G. H., J. E. Littlewood, G. Pólya, Inequalities, 2nd edition, Cambridge University Press, Cambridge, 1959.
- Padmanabhan, S., V. Lokesha, M. Saraj and K. M. Nagaraja, Oscillatory mean for several positive arguments, Journal of intelligent system research, Vol. 2, 2008, No. 2, 137–139.
- Czinder, P., Z. Pales, An extension of the Hermite-Hadamard inequality and an application for Gini and Stolarsky means, JIPAM, Vol. 5, 2004, No. 2, Article No. 42.
- Sándor, J., M. Bencze, An application of Gauss Quadrature Formula, Octogon. Mathematical Magazine, Vol. 15, 2007, No. 1, 276–279.
- Wang, S., Y. Chu, The best bounds of combination of arithmetic and harmonic means for the Seiffert’s mean, Int. J. Math. Analysis, Vol. 4, 2010, No. 22, 1079–1084.
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Cite this paper
Nagaraja, K. M. & Siva Kota Reddy, P. (2012). Double inequalities on means via quadrature formula. Notes on Number Theory and Discrete Mathematics, 18(1), 22-28.