On some Hermite-Hadamard type inequalities for twice differentiable mappings and applications

  • U. S. Kirmaci
  • R. Dikici
Keywords: Convex functions, Hölder’s inequality, Grüss’ inequality, Chebychev’s inequality, Bullen’s inequality, Special means.

Abstract

Some inequalities for twice differentiable mappings are presented. Some applications to special means of real numbers are also given.

Author Biographies

U. S. Kirmaci
K. K. Education Faculty Department of Mathematics, Atatürk University, 25240 Erzurum, Turkey.
R. Dikici
K. K. Education Faculty Department of Mathematics, Atatürk University, 25240 Erzurum, Turkey.

References

S. S. Dragomir, Selected Topics on Hermite-Hadamard Inequalities and Applications,

http://rgmia.vu.edu.au/SSDragomirWeb.html.

U. S. Kirmaci, M. K. Bakula, M. E. Ozdemir and J. E. Pev caric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput.,193(2007), 26--35.

U. S. Kirmaci, Improvement and further generalization of inequalities for differentiable mappings and applications, Comput. Math. Appl., 55(2008), 485--493.

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 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), 361--368.

U. S. Kirmaci and M. E. Ozdemir, Some inequalities for mappings whose derivatives are bounded and applications to special means of real numbers, Appl.

Math. Lett., 17 (2004), 641--645.

D.S. Mitrinovic Analytic Inequalities, Springer-Verlag New-York, Heidelberg, Berlin, 1970.

Published
2013-03-22
How to Cite
Kirmaci, U. S., & Dikici, R. (2013). On some Hermite-Hadamard type inequalities for twice differentiable mappings and applications. Tamkang Journal of Mathematics, 44(1), 41-51. https://doi.org/10.5556/j.tkjm.44.2013.964
Section
Papers