A NOTE ON OSTROWSKI TYPE INEQUALITIES RELATED TO SOME s-CONVEX FUNCTIONS IN THE SECOND SENSE

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 4, 2012, pp.775-785
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.4.775

Title & Authors

A NOTE ON OSTROWSKI TYPE INEQUALITIES RELATED TO SOME s-CONVEX FUNCTIONS IN THE SECOND SENSE

Liu, Zheng;

Liu, Zheng;

Abstract

Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.

Keywords

Ostrowski type inequality;convex function;s-convex function;Hlder inequality;averaged midpoint-trapezoid inequality;

Language

English

Cited by

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References

1.

M. Alomari, M. Darus, S. S. Dragomir, and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett. 23 (2010), no. 1, 1071-1076.

2.

S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), no. 5, 91-95.

3.

S. S. Dragomir, P. Cerone, and J. Roumeliotis, A new generalization of Ostrowski integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett. 13 (2000), no. 1, 19-25.

4.

H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), no. 1, 100-111.

5.

U. S. Kirmaci, M. K. Bakula, M. E. Ozdemir, and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (2007), no. 1, 26-35.

6.

C. E. M. Pearce and J. Pecaric, Inequalities for differentiable mappings with applications to special means and quadrature formulae, Appl. Math. Lett. 13 (2000), no. 2, 51-55.