Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are *P*-Convex

Affiliation(s)

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

School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, China.

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

School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, China.

ABSTRACT

In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are*P*-convex.

In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are

Cite this paper

B. Xi, S. Wang and F. Qi, "Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are*P*-Convex," *Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1898-1902. doi: 10.4236/am.2012.312260.

B. Xi, S. Wang and F. Qi, "Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are

References

[1] S. S. Dragomir, J. Pe?ari? and L. E. Persson, “Some Inequalities of Hadamard Type,” Soochow Journal of Mathematics, Vol. 21, No. 3, 1995, pp. 335-341.

[2] 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, 1998, pp. 91-95. doi:10.1016/S0893-9659(98)00086-X

[3] M. Alomari and S. Hussain, Two Inequalities of Simpson Type for Quasi-Convex Functions and Applications, Applied Mathematics E-Notes, Vol. 11, 2011, pp. 110-117.

[4] L. Chun and F. Qi, “Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are s-Convex,” Applied Mathematics, Vol. 3, No. 11, 2012, pp. 1680-1685. doi:10.4236/am.2012.311232

[5] S. S. Dragomir and C. E. M. Pearce, “Selected Topics on Hermite-Hadamard Type Inequalities and Applications,” RGMIA Monographs, Victoria University, Melbourne, 2000.

[6] W.-D. Jiang, D.-W. Niu, Y. Hua, and F. Qi, “Generalizations of Hermite-Hadamard Inequality to n-Time Differentiable Functions Which Are s-Convex in the Second Sense,” Analysis (Munich), Vol. 32, No. 3, 2012, pp. 209-220. doi:10.1524/anly.2012.1161

[7] U. S. Kirmaci, “Inequalities for Differentiable Mappings and Applications to Special Means of Real Numbers to Midpoint Formula,” Applied Mathematics and Computation, Vol. 147, No. 1, 2004, pp. 137-146. doi:10.1016/S0096-3003(02)00657-4

[8] C. P. Niculescu and L.-E. Persson, “Convex Functions and Their Applications,” Springer-Verlag, New York, 2005.

[9] C. E. M. Pearce and J. Pe?ari?, “Inequalities for Differentiable Mappings with Application to Special Means and Quadrature Formulae,” Applied Mathematics Letters, Vol. 13, No. 2, 2000, pp. 51-55. doi:10.1016/S0893-9659(99)00164-0

[10] F. Qi, Z.-L. Wei and Q. Yang, “Generalizations and Refinements of Hermite-Hadamard’s Inequality,” Rocky Mountain Journal of Mathematics, Vol. 35, No. 1, 2005, pp. 235-251. doi:10.1216/rmjm/1181069779

[11] S.-H. Wang, B.-Y. Xi and F. Qi, “Some New Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions Which Are m-Convex,” Analysis (Munich), Vol. 32, No. 3, 2012, pp. 247-262. doi:10.1524/anly.2012.1167

[12] B.-Y. Xi, R.-F. Bai and F. Qi, “Hermite-Hadamard Type Inequalities for the m-and (a,m)-Geometrically Convex Functions,” Aequationes Mathematicae, Vol. 84, No. 3, 2012, pp. 261-269. doi:10.1007/s00010-011-0114-x

[13] B.-Y. Xi and F. Qi, “Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means,” Journal of Function Spaces and Applications, Vol. 2012, 2012, Article ID: 980438, p 14. doi:10.1155/2012/980438

[14] T.-Y. Zhang, A.-P. Ji and F. Qi, “On Integral Inequalities of Hermite-Hadamard Type for s-Geometrically Convex Functions,” Abstract and Applied Analysis, Vol. 2012, 2012, Article ID: 560586, p 14. doi:10.1155/2012/560586

[1] S. S. Dragomir, J. Pe?ari? and L. E. Persson, “Some Inequalities of Hadamard Type,” Soochow Journal of Mathematics, Vol. 21, No. 3, 1995, pp. 335-341.

[2] 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, 1998, pp. 91-95. doi:10.1016/S0893-9659(98)00086-X

[3] M. Alomari and S. Hussain, Two Inequalities of Simpson Type for Quasi-Convex Functions and Applications, Applied Mathematics E-Notes, Vol. 11, 2011, pp. 110-117.

[4] L. Chun and F. Qi, “Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are s-Convex,” Applied Mathematics, Vol. 3, No. 11, 2012, pp. 1680-1685. doi:10.4236/am.2012.311232

[5] S. S. Dragomir and C. E. M. Pearce, “Selected Topics on Hermite-Hadamard Type Inequalities and Applications,” RGMIA Monographs, Victoria University, Melbourne, 2000.

[6] W.-D. Jiang, D.-W. Niu, Y. Hua, and F. Qi, “Generalizations of Hermite-Hadamard Inequality to n-Time Differentiable Functions Which Are s-Convex in the Second Sense,” Analysis (Munich), Vol. 32, No. 3, 2012, pp. 209-220. doi:10.1524/anly.2012.1161

[7] U. S. Kirmaci, “Inequalities for Differentiable Mappings and Applications to Special Means of Real Numbers to Midpoint Formula,” Applied Mathematics and Computation, Vol. 147, No. 1, 2004, pp. 137-146. doi:10.1016/S0096-3003(02)00657-4

[8] C. P. Niculescu and L.-E. Persson, “Convex Functions and Their Applications,” Springer-Verlag, New York, 2005.

[9] C. E. M. Pearce and J. Pe?ari?, “Inequalities for Differentiable Mappings with Application to Special Means and Quadrature Formulae,” Applied Mathematics Letters, Vol. 13, No. 2, 2000, pp. 51-55. doi:10.1016/S0893-9659(99)00164-0

[10] F. Qi, Z.-L. Wei and Q. Yang, “Generalizations and Refinements of Hermite-Hadamard’s Inequality,” Rocky Mountain Journal of Mathematics, Vol. 35, No. 1, 2005, pp. 235-251. doi:10.1216/rmjm/1181069779

[11] S.-H. Wang, B.-Y. Xi and F. Qi, “Some New Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions Which Are m-Convex,” Analysis (Munich), Vol. 32, No. 3, 2012, pp. 247-262. doi:10.1524/anly.2012.1167

[12] B.-Y. Xi, R.-F. Bai and F. Qi, “Hermite-Hadamard Type Inequalities for the m-and (a,m)-Geometrically Convex Functions,” Aequationes Mathematicae, Vol. 84, No. 3, 2012, pp. 261-269. doi:10.1007/s00010-011-0114-x

[13] B.-Y. Xi and F. Qi, “Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means,” Journal of Function Spaces and Applications, Vol. 2012, 2012, Article ID: 980438, p 14. doi:10.1155/2012/980438

[14] T.-Y. Zhang, A.-P. Ji and F. Qi, “On Integral Inequalities of Hermite-Hadamard Type for s-Geometrically Convex Functions,” Abstract and Applied Analysis, Vol. 2012, 2012, Article ID: 560586, p 14. doi:10.1155/2012/560586