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SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS

Year 2011, Volume: 40 Issue: 2, 219 - 229, 01.02.2011

Abstract

In this paper, we establish some new Hermite-Hadamard type inequalities for m-convex and (α, m)-convex functions of 2-variables on the co-ordinates

References

  • Alomari, M. and Darus, M. Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sciences 3 (32), 1557–1567, 2008.
  • Bakula, M. K. ¨Ozdemir, M. E. and Peˇcari´c, J. Hadamard type inequalities for m-convex and (α, m)-convex functions, J. Inequal. Pure and Appl. Math. 9 (4), Art. 96, 2008.
  • Bakula, M. K., Peˇcari´c, J. and Ribiˇci´c, M. Companion inequalities to Jensen’s inequality for m-convex and(α, m)-convex functions, J. Inequal. Pure and Appl. Math. 7 (5), Art. 194, 2006.
  • Dragomir, S. S. On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics 4, 775–788, 2001.
  • Dragomir, S. S. and Pearce, C. E. M. Selected Topics on Hermite-Hadamard Inequal- itiesand Applications http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
  • Victoria University, 2000). [Online:
  • Dragomir, S. S. and Toader, G. Some inequalities for m-convex functions, Studia Univ. Babes- Bolyai, Mathematica 38 (1), 21–28, 1993.
  • Mihe¸san, V. G. A generalization of the convexity (Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, Romania, 1993).
  • Toader, G. Some generalizations of the convexity, Proc. Colloq. Approx. Opt. Cluj-Napoca, 329–338, 1984.
  • Set, E., Sardari, M., Ozdemir, M. E. and Rooin, J. On generalizations of the Hadamard inequality for(α, m)-convex functions, RGMIA Res. Rep. Coll. 12 (4), Article 4, 2009.

SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS

Year 2011, Volume: 40 Issue: 2, 219 - 229, 01.02.2011

Abstract

References

  • Alomari, M. and Darus, M. Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sciences 3 (32), 1557–1567, 2008.
  • Bakula, M. K. ¨Ozdemir, M. E. and Peˇcari´c, J. Hadamard type inequalities for m-convex and (α, m)-convex functions, J. Inequal. Pure and Appl. Math. 9 (4), Art. 96, 2008.
  • Bakula, M. K., Peˇcari´c, J. and Ribiˇci´c, M. Companion inequalities to Jensen’s inequality for m-convex and(α, m)-convex functions, J. Inequal. Pure and Appl. Math. 7 (5), Art. 194, 2006.
  • Dragomir, S. S. On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics 4, 775–788, 2001.
  • Dragomir, S. S. and Pearce, C. E. M. Selected Topics on Hermite-Hadamard Inequal- itiesand Applications http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
  • Victoria University, 2000). [Online:
  • Dragomir, S. S. and Toader, G. Some inequalities for m-convex functions, Studia Univ. Babes- Bolyai, Mathematica 38 (1), 21–28, 1993.
  • Mihe¸san, V. G. A generalization of the convexity (Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, Romania, 1993).
  • Toader, G. Some generalizations of the convexity, Proc. Colloq. Approx. Opt. Cluj-Napoca, 329–338, 1984.
  • Set, E., Sardari, M., Ozdemir, M. E. and Rooin, J. On generalizations of the Hadamard inequality for(α, m)-convex functions, RGMIA Res. Rep. Coll. 12 (4), Article 4, 2009.
There are 10 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

M.e. Özdemir This is me

E. Set This is me

Erhan Set This is me

 m.z. Sarıkaya This is me

Publication Date February 1, 2011
Published in Issue Year 2011 Volume: 40 Issue: 2

Cite

APA Özdemir, M., Set, E., Set, E., Sarıkaya, . (2011). SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics, 40(2), 219-229.
AMA Özdemir M, Set E, Set E, Sarıkaya . SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics. February 2011;40(2):219-229.
Chicago Özdemir, M.e., E. Set, Erhan Set, and  m.z. Sarıkaya. “SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED M-CONVEX AND (α, M)-CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics 40, no. 2 (February 2011): 219-29.
EndNote Özdemir M, Set E, Set E, Sarıkaya  (February 1, 2011) SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics 40 2 219–229.
IEEE M. Özdemir, E. Set, E. Set, and  . Sarıkaya, “SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, pp. 219–229, 2011.
ISNAD Özdemir, M.e. et al. “SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED M-CONVEX AND (α, M)-CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics 40/2 (February 2011), 219-229.
JAMA Özdemir M, Set E, Set E, Sarıkaya . SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics. 2011;40:219–229.
MLA Özdemir, M.e. et al. “SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED M-CONVEX AND (α, M)-CONVEX FUNCTIONS”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, 2011, pp. 219-2.
Vancouver Özdemir M, Set E, Set E, Sarıkaya . SOME NEW HADAMARD TYPE INEQUALITIES FOR CO-ORDINATED m-CONVEX AND (α, m)-CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics. 2011;40(2):219-2.