Abstract and Applied Analysis

On Integral Inequalities of Hermite-Hadamard Type for s-Geometrically Convex Functions

Tian-Yu Zhang, Ai-Ping Ji, and Feng Qi

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Abstract

The authors introduce the concept of the s-geometrically convex functions. By the well-known Hölder inequality, they establish some integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions and apply these inequalities to special means.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 560586, 14 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475831

Digital Object Identifier
doi:10.1155/2012/560586

Mathematical Reviews number (MathSciNet)
MR2975277

Zentralblatt MATH identifier
1253.26047

Citation

Zhang, Tian-Yu; Ji, Ai-Ping; Qi, Feng. On Integral Inequalities of Hermite-Hadamard Type for s -Geometrically Convex Functions. Abstr. Appl. Anal. 2012 (2012), Article ID 560586, 14 pages. doi:10.1155/2012/560586. https://projecteuclid.org/euclid.aaa/1364475831


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References

  • H. Hudzik and L. Maligranda, “Some remarks on $s$-convex functions,” Aequationes Mathematicae, vol. 48, no. 1, pp. 100–111, 1994.
  • S. S. Dragomir and R. P. Agarwal, “Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula,” Applied Mathematics Letters, vol. 11, no. 5, pp. 91–95, 1998.
  • U. S. Kirmaci, “Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,” Applied Mathematics and Computation, vol. 147, no. 1, pp. 137–146, 2004.
  • U. S. Kirmaci, M. Klaričić Bakula, M. E. Özdemir, and J. Pečarić, “Hadamard-type inequalities for $s$-convex functions,” Applied Mathematics and Computation, vol. 193, no. 1, pp. 26–35, 2007.
  • S. Hussain, M. I. Bhatti, and M. Iqbal, “Hadamard-type inequalities for $s$-convex functions. I,” Punjab University. Journal of Mathematics, vol. 41, pp. 51–60, 2009.
  • M. W. Alomari, M. Darus, and U. S. Kirmaci, “Some inequalities of Hermite-Hadamard type for $s$-convex functions,” Acta Mathematica Scientia B, vol. 31, no. 4, pp. 1643–1652, 2011.