Double inequalities on means via quadrature formula

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

  1. Bullen, P. S. Handbook of means and their inequalities, Kluwer Acad. Publ., Dordrecht, 2003.
  2. Hardy, G. H., J. E. Littlewood, G. Pólya, Inequalities, 2nd edition, Cambridge University Press, Cambridge, 1959.
  3. 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.
  4. 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.
  5. Sándor, J., M. Bencze, An application of Gauss Quadrature Formula, Octogon. Mathematical Magazine, Vol. 15, 2007, No. 1, 276–279.
  6. 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

APA

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.

Chicago

Nagaraja, K. M. and P. Siva Kota Reddy. “Double Inequalities on Means via Quadrature Formula.” Notes on Number Theory and Discrete Mathematics 18, no. 1 (2012): 22-28.

MLA

Nagaraja, K. M. and P. Siva Kota Reddy. “Double Inequalities on Means via Quadrature Formula.” Notes on Number Theory and Discrete Mathematics 18.1 (2012): 22-28. Print.

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