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

Affiliation(s)

College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China.

College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China.

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.

The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for

Cite this paper

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.

L. Han and G. Liu, "Integral Inequalities of Hermite-Hadamard Type for

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

[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