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GENERALIZATION OF THE FEJÉR-HADAMARD'S INEQUALITY FOR CONVEX FUNCTION ON COORDINATES

  • Farid, Ghulam (COMSATS Institute of Information Technology Attock Campus) ;
  • Rehman, Atiq Ur (COMSATS Institute of Information Technology Attock Campus)
  • Received : 2015.03.13
  • Published : 2016.01.31

Abstract

In this paper, we give generalization of the $Fej\acute{e}r$-Hadamard inequality by using definition of convex functions on n-coordinates. Results given in [8, 12] are particular cases of results given here.

Keywords

References

  1. S. Abramovich, G. Farid, and J. Pecaric, More about Jensen's inequality and Cauchy's means for superquadratic functions, J. Math. Inequal. 7 (2013), no. 1, 11-14.
  2. S. Banic, Mappings connected with Hermite-Hadamard inequalities for superquadratic functions, J. Math. Inequal. 3 (2009), no. 4, 577-589.
  3. S. I. Butt, J. Pecaric, and A. U. Rehman, Non-symmetric Stolarsky means, J. Math. Inequal. 7 (2013), no. 2, 227-237.
  4. F. Chen and S. Wu, Hermite-Hadamard type inequalities for harmonically s-convex functions, Sci. World J. 2014 (2014), no. 7, Article ID 279158.
  5. S. S. Dragomir, A mapping in connection to Hadamard's inequalities, Anz. Osterreich. Akad. Wiss. Math.-Natur. Kl. 128 (1991), no. 2, 17-20.
  6. S. S. Dragomir, On Hadamard's inequalities for convex functions, Math. Balkanica (N.S.) 6 (1992), no. 3, 215-222.
  7. S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl. 167 (1992), no. 1, 49-56. https://doi.org/10.1016/0022-247X(92)90233-4
  8. 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. https://doi.org/10.11650/twjm/1500574995
  9. S. S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones 34 (2015), no. 4, 323-341. https://doi.org/10.4067/S0716-09172015000400002
  10. S. S. Dragomir and A. McAndrew, Refinements of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 6 (2005), no. 5, Article 140, 6 pp.
  11. S. S. Dragomir, J. E. Pecaric, and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), no. 3, 335-341.
  12. G. Farid, M. Marwan, and A. U. Rehman, Fejer-Hadamard inequality for convex functions on the coordinates in a rectangle from the plane, Int. J. Analysis Appl. 10 (2016), no. 1, 40-47.
  13. L. Fejer, Uber die Fourierreihen. II, Math. Naturwiss Anz Ungar. Akad.Wiss. 24 (1906), 369-390.
  14. D.-Y. Hwang, K.-L. Tseng, and G.-S. Yang, Some Hadamard's inequalities for coordinated convex functions in a rectangle from the plane, Taiwanese J. Math. 11 (2007), no. 1, 63-73. https://doi.org/10.11650/twjm/1500404635
  15. M. A. Noor, K. I. Noor, and M. U. Awan, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Equ. 60 (2015), no. 6, 776-786. https://doi.org/10.1080/17476933.2014.976814
  16. M. A. Noor, F. Qi, and M. U. Awan, Some Hermite-Hadamard type inequalities for log-h-convex functions, Analysis (Berlin) 33 (2013), no. 4, 367-375.
  17. J. E. Pecaric, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, New York, 1992.
  18. M. Tunc, On some new inequalities for convex functions, Turkish J. Math. 36 (2012), no. 2, 245-251.

Cited by

  1. A Generalized Hermite-Hadamard Inequality for Coordinated Convex Function and Some Associated Mappings vol.2016, 2016, https://doi.org/10.1155/2016/1631269