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

  • Liu, Zheng (Institute of Applied Mathematics School of Science University of Science and Technology Liaoning)
  • Received : 2011.04.08
  • Published : 2012.07.31

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

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. https://doi.org/10.1016/j.aml.2010.04.038
  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. https://doi.org/10.1016/S0893-9659(98)00086-X
  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. https://doi.org/10.1016/S0893-9659(99)00139-1
  4. H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), no. 1, 100-111. https://doi.org/10.1007/BF01837981
  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. https://doi.org/10.1016/j.amc.2007.03.030
  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. https://doi.org/10.1016/S0893-9659(99)00164-0

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  3. INEQUALITIES FOR THE RIEMANN-STIELTJES INTEGRAL OF PRODUCT INTEGRATORS WITH APPLICATIONS vol.51, pp.4, 2014, https://doi.org/10.4134/JKMS.2014.51.4.791
  4. Remarks on some inequalities for s-convex functions and applications vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0851-9
  5. On new general integral inequalities for s-convex functions vol.246, 2014, https://doi.org/10.1016/j.amc.2014.08.041
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