| | | |

## entrSome Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and ApplicationsSome Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications

#### Bo-Yan Xi [1] , Feng Qi [2]

##### 147 475

In the paper, the authors offer some new inequalities for differentiableconvex functions, which are connected with Hermite-Hadamard integralinequality, and apply these inequalities to special means of two positivenumbers.
Integral inequality, Hermite-Hadamard integral inequality, Convex function, Mean, Application2000 AMS Classification:26D15, 26A51, 26D20, 26E60, 41A55.
• Bai, R.-F., Qi, F. and Xi, B.-Y. Hermite-Hadamard type inequalities for the m- and (α, m)logarithmically convex functions, Filomat 27 (1), 1–7, 2013.
• Dragomir, S. S. and Agarwal, R. P. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (5), 91–95, 1998.
• Dragomir, S. S., Agarwal, R. P. and Cerone, P. On Simpson’s inequality and applications, J. Inequal. Appl. 5 (6), 533–579, 2000.
• Kirmaci, U. S. Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput. 147 (1), 137–146, 2004. Mitrinovi´ c, D. S. Analytic Inequalities, Springer-Verlag, Berlin, 1970.
• Pearce, C. E. M. and Peˇ cari´ c, J. Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett. 13 (2), 51–55, 2000.
• Qi, F. Bounds for the ratio of two gamma functions, J. Inequal. Appl. 2010, Article ID 493058, 84 pages, 2010.
• Qi, F., Wei, Z.-L. and Yang, Q. Generalizations and refinements of Hermite-Hadamard’s inequality, Rocky Mountain J. Math. 35 (1), 235–251, 2005.
• Wang, S.-H., Xi, B.-Y. and Qi, F. On Hermite-Hadamard type inequalities for (α, m)-convex functions, Int. J. Open Probl. Comput. Sci. Math. 5 (4), 47–56, 2012.
• Wang, S.-H., Xi, B.-Y. and Qi, F. Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich) 32 (3), 247–262, 20 Xi, B.-Y., Bai, R.-F. and Qi, F. Hermite-Hadamard type inequalities for the m- and (α, m)geometrically convex functions, Aequationes Math. 84 (3), 261–269, 2012.
• Xi, B.-Y. and Qi, F. Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl. 2012, Article ID 980438, 14 pages, 20
Primary Language tr Mathematics Author: Bo-Yan Xi Author: Feng Qi
 Bibtex @ { hujms101277, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2013}, volume = {42}, pages = {243 - 257}, doi = {}, title = {Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications}, key = {cite}, author = {Xi, Bo-Yan and Qi, Feng} } APA Xi, B , Qi, F . (2013). Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications. Hacettepe Journal of Mathematics and Statistics, 42 (3), 243-257. Retrieved from http://dergipark.gov.tr/hujms/issue/7748/101277 MLA Xi, B , Qi, F . "Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications". Hacettepe Journal of Mathematics and Statistics 42 (2013): 243-257 Chicago Xi, B , Qi, F . "Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications". Hacettepe Journal of Mathematics and Statistics 42 (2013): 243-257 RIS TY - JOUR T1 - Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications AU - Bo-Yan Xi , Feng Qi Y1 - 2013 PY - 2013 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 243 EP - 257 VL - 42 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications %A Bo-Yan Xi , Feng Qi %T Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications %D 2013 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 42 %N 3 %R %U ISNAD Xi, Bo-Yan , Qi, Feng . "Some Hermite-Hadamard Type Inequalities for DifferentiableConvex Functions and Applications". Hacettepe Journal of Mathematics and Statistics 42 / 3 (March 2013): 243-257.