Main Article Content
In this paper, new integral inequalities of Hermite-Hadamard type are developed for n-times differentiable convex functions. Also a parallel development is made base on concavity.
- S.-P. Bai, S.-H. Wang and F. Qi, Some Hermite-Hadamard type inequalities for n-time differentiable (α,m)-convex functions, J. Inequal. Appl. 2012 (2012), Article ID 267.
- P. Cerone, S.S. Dragomir and J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstr. Math. 32 (4) (1999), 697-712.
- P. Cerone, S.S. Dragomir and J. Roumeliotis and J. Sunde, A new generalization of the trapezoid formula for n-time differentiable mappings and applications, Demonstr. Math. 33 (4) (2000), 719-736.
- S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. Online:[http://www.staxo.vu.edu.au/RGMIA/monographs/hermitehadamard.html].
- D.-Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. J. 43 (2003), 335-343.
- J. L. W. V. Jensen, On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B., 16 (1905), 49-69.
- W.-D. Jiang, D.-W. Niu, Y. Hua and F. Qi, Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s-convex in the second sense, Analysis (Munich), 32 (2012), 209-220.
- H. Kavurmaci, M. Avci, M.E. Ozdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, J. Inequal. Appl. 2011 (2011), Article ID 86.
- U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147 (2004), 137-146.
- U.S. Kirmaci, M.K. Bakula, M.E. Ozdemir and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193 (2007), 26-35.
- M.E. Ozdemir and U.S. Kirmaci, Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comput. 143 (2003), 269-274.
- M.E. Ozdemir, C. Yildiz, New Inequalities for n-time differentiable functions, Arxiv:1402.4959v1.
- M.E. Ozdemir, C. Yildiz, New Inequalities for Hermite-Hadamard and Simpson Type with Applications, Tamkang J. Math. 44 (2) (2013) 209-216.
- A. Saglam, M.Z Sarikaya and H. Yildirim, Some new inequalities of Hermite-Hadamard's type, Kyung. Math. J. 50 (2010), 399-410.
- M.Z. Sarikaya and N. Aktan, On the generalization some integral inequalities and their applications, Math. Comput. Modelling, 54 (2011), 2175-2182.
- E. Set, M.E. Ozdemir and S.S. Dragomir, On Hadamard-Type Inequalities Involving Several Kinds of Convexity, J. Inequal. Appl. 2010 (2010) Article ID 286845.
- C ¸. Yildiz, New Inequalities of the Hermite-Hadamard type for n-time differentiable functions which are quasiconvex, J. Math. Inequal. (10) (3) (2016), 703-711.
- 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), 32 (2012), 247-262.
- B.-Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl., 2012 (2012), Article ID 980438.