1Department of Business Administration, Aletheia University, Tamsui, New Taipei City 25103, Taiwan.
2China University of Science and Technology, Nankang, Taipei 11522, Taiwan.
3Department of Applied Mathematics, Aletheia University, Tamsui, New Taipei City 25103, Taiwan.
Abstract
In this paper, we shall establish some extended Simpson-type inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Simpson formula are also given.
M. Alomari and M. Darus, On the Hadamard's inequality for log-convex functions on the coordinates, J. Inequal. Appl. 2009 (2009), Article ID 283147, 17 pages.
S.S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl.167 (1992), no. 1, 49--56.
S.S. Dragomir, On the Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math.5 (2001), no. 4, 775--788.
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. textbf11 (1998), no. 5, 91--95.
S.S. Dragomir, R.P. Agarwal and P. Cerone, On Simpson's inequality and applications, J. Inequal. Appl. 5 (2000), no. 6, 533--579.
S.S. Dragomir, Y.J. Cho and S.S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, J. Math. Anal. Appl.245 (2000), no. 2, 489--501.
J. Hadamard, étude sur les propriétés des fonctions entiéres en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl. 58 (1893) 171--215.
U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput.147 (2004), no. 1, 137--146.
U.S. Kirmaci and M.E. Ozdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput.153 (2004), no. 2, 361--368.
C.E.M. Pearce and J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formulæ, Appl. Math. Lett. 13 (2000)), no. 2, 51--55.
G.S. Yang and K.L. Tseng, Inequalities of Hermite-Hadamard-Fejér type for convex functions and Lipschitzian functions, Taiwanese J. Math.7 (2003), no. 3, 433--440.
Top