Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

[1] M. Alomari and M. Darus, Fejer inequality for double integrals, Facta Universitatis (NIŠ): Ser.v Math. Inform. 24(2009), 15-28.Search in Google Scholar

[2] M. Alomari, M. Darus, U.S. Kirmaci, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Computers & Mathematics with Applications, Volume 59, Issue 1, January 2010, Pages 225-23210.1016/j.camwa.2009.08.002Search in Google Scholar

[3] S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to Trapezoidal formula, Appl. Math. Lett. 11(5) (1998) 91-95.10.1016/S0893-9659(98)00086-XSearch in Google Scholar

[4] S.S. Dragomir, On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 4 (2001), 775-788.Search in Google Scholar

[5] S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, Journal of Mathematical Analysis and Applications, 167, 49-56. http://dx.doi.org/10.1016/0022-247X(92)90233-410.1016/0022-247X(92)90233-4Search in Google Scholar

[6] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequal- ities and Applications, RGMIA Monographs, Victoria University, 2000. Online: [http://www.staff.vu.edu.au/RGMIA/monographs/hermitehadamard.html].Search in Google Scholar

[7] J. Hadamard, Étude sur les Propriétés des Fonctions Entières en Particulier d'une Fonction Considérée par Riemann. Journal de Mathématiques Pures et Appliquées, 58, 171-215.Search in Google Scholar

[8] D. Y. Hwang, K. L. Tseng, and G. S. Yang, Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese Journal of Mathematics, 11(2007), 63-73.10.11650/twjm/1500404635Search in Google Scholar

[9] D. Y. Hwang, Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables, Applied Mathematics and Computation 217 (2011) 9598{9605.Search in Google Scholar

[10] D. -Y. Hwang, K.-C. Hsu and K.-L. Tseng, Hadamard-Type inequalities for Lipschitzian functions in one and two variables with applications, Journal of Mathematical Analysis and Applications, 405, 546-554. http://dx.doi.org/10.1016/j.jmaa.2013.04.032.10.1016/j.jmaa.2013.04.032Search in Google Scholar

[11] K.-C. Hsu, Some Hermite-Hadamard type inequalities for diffrentiable co-ordinated convex functions and applications, Advances in Pure Mathematics, 2014, 4, 326-340.10.4236/apm.2014.47044Search in Google Scholar

[12] K.-C. Hsu, Refinements of Hermite-Hadamard type inequalities for differentiable coordinated convex functions and applications, Taiwanese Journal of Mathematics, (In press). http://dx.doi.org/10.1142/9261.10.1142/9261Search in Google Scholar

[13] M. A. Latif and M. Alomari, Hadamard-type inequalities for product of two convex functions on the co-ordinates, Int. Math. Forum, 4(47), 2009, 2327-2338.Search in Google Scholar

[14] M. A. Latif and M. Alomari, On the Hadamard-type inequalities for h-convex functions on the co-ordinates, Int. J. of Math. Analysis, 3(33), 2009, 1645-1656.Search in Google Scholar

[15] M. A. Latif, S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, Journal of Inequalities and Applications 2012, 2012:28.10.1186/1029-242X-2012-28Search in Google Scholar

[16] M. A. Latif, S. Hussain and S. S. Dragomir, Refinements of Hermite-Hadamard type inequalities for co-ordinated quasi-convex functions, International Journal of Mathematical Archive-3(1), 2012, 161-171.Search in Google Scholar

[17] S.-L. Lyu, On the Hermite-Hadamard inequality for convex functions of two variable, Numerical Algebra, Control and Optimization, Volume 4, Number 1, March 2014.10.3934/naco.2014.4.1Search in Google Scholar

[18] M.E. Özdemir, E. Set and M.Z. Sarikaya, New some Hadamard's type inequalities for co-ordinated m-convex and (_ ;m)-convex functions, Hacettepe Journal of Mathematics and Statistics 40 (2), 219-229.Search in Google Scholar

[19] M.E. Özdemir, M. A. Latif and A. O. Akdemir, On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, Journal of Inequalities and Applications 2012, 2012:21. doi:10.1186/1029-242X-2012-21.Search in Google Scholar

[20] M.E. Özdemir, A. O. Akdemir, Ağrı, C. Yıdız and Erzurum, On co-ordinated quasi-convex functions, Czechoslovak Mathematical Journal, 62 (137) (2012), 889-900.10.1007/s10587-012-0072-zSearch in Google Scholar

[21] C. M. E. Pearce and J. E. Pečarić, Inequalities for differentiable mappings with applications to special means and quadrature formula, Appl. Math. Lett. 13 (2000) 51-55.10.1016/S0893-9659(99)00164-0Search in Google Scholar

[22] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Ordering and Statistical Applications, Academic Press, New York, 1991.Search in Google Scholar

[23] M.Z. Sarikaya, E. Set, M.E. Özdemir and S. S. Dragomir, New some Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences 28(2) (2012) 137-152.Search in Google Scholar