Integral Inequalities of Hermite-Hadamard Type for r-Convex Functions

DOI: 10.4236/am.2012.312270   PDF   HTML   XML   3,406 Downloads   5,288 Views   Citations

Abstract

The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.

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L. Han and G. Liu, "Integral Inequalities of Hermite-Hadamard Type for r-Convex Functions," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1967-1971. doi: 10.4236/am.2012.312270.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] C. E. M. Pearce, J. Peccaric and V. Simic, “Stolarsky Means and Hadamard’s Inequality,” Journal of Mathematical Analysis and Applications, Vol. 220, No. 1, 1998, pp. 99-109. doi:10.1006/jmaa.1997.5822
[2] G.-S. Yang, “Refinements of Hadamard’s Inequality for r-Convex Functions,” Indian Journal of Pure and Applied Mathematics, Vol. 32, No. 10, 2001, pp. 1571-1579.
[3] N. P. N. Ngoc, N. V. Vinh and P. T. T. Hien, “Integral Inequalities of Hadamard Type for r-Convex Functions,” International Mathematical Forum, Vol. 4, No. 35, 2009, pp. 1723-1728.
[4] M. K. Bakula, M. E. Ozdemir and J. Pecaric, “Hadamard Type Inequalities for m-Convex and (α-m)-Convex Functions,” Journal of Inequalities in Pure and Applied Mathematics, Vol. 9, No. 4, 2008, Article ID: 96.
[5] P. M. Gill, C. E. M. Pearce and J. Pe?ari?, “Hadamard’s Inequality for r-Convex Functions,” Journal of Mathematical Analysis and Applications, Vol. 215, No. 2, 1997, pp. 461-470. doi:10.1006/jmaa.1997.5645
[6] A. G. Azpeitia, “Convex Functions and the Hadamard Inequality,” Revista Colombiana de Matemáticas, Vol. 28, No. 1, 1994, pp. 7-12.
[7] K. B. Stolarsky, “Generalizations of the Logarithmic Mean,” Mathematics Magazine, Vol. 48, No. 2, 1975, pp. 87-92. doi:10.2307/2689825

  
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