On Generalized Inequalities of Hermite-Hadamard Type for Convex Functions

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Cetin Yildiz, M. Emin Ozdemir

Abstract

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.

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References

  1. 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.
  2. 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.
  3. 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.
  4. 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].
  5. D.-Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. J. 43 (2003), 335-343.
  6. J. L. W. V. Jensen, On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B., 16 (1905), 49-69.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. M.E. Ozdemir, C. Yildiz, New Inequalities for n-time differentiable functions, Arxiv:1402.4959v1.
  13. M.E. Ozdemir, C. Yildiz, New Inequalities for Hermite-Hadamard and Simpson Type with Applications, Tamkang J. Math. 44 (2) (2013) 209-216.
  14. A. Saglam, M.Z Sarikaya and H. Yildirim, Some new inequalities of Hermite-Hadamard's type, Kyung. Math. J. 50 (2010), 399-410.
  15. M.Z. Sarikaya and N. Aktan, On the generalization some integral inequalities and their applications, Math. Comput. Modelling, 54 (2011), 2175-2182.
  16. 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.
  17. 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.
  18. 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.
  19. 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.