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Journal of Mathematics
Volume 2017 (2017), Article ID 3634693, 8 pages
https://doi.org/10.1155/2017/3634693
Research Article

Some Hermite-Hadamard-Fejér Type Integral Inequalities for Differentiable -Convex Functions with Applications

1Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
2Institute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia), Apartado 644, 48080 Bilbao, Spain

Correspondence should be addressed to M. Rostamian Delavar; ri.ca.bu@naimatsor.m

Received 8 March 2017; Revised 20 July 2017; Accepted 5 November 2017; Published 21 November 2017

Academic Editor: Ji Gao

Copyright © 2017 M. Rostamian Delavar and M. De La Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Fejér, “Über die fourierreihen, II,” Math. Naturwise. Anz Ungar. Akad. Wiss, vol. 2, pp. 369–390, 1906. View at Google Scholar
  2. M. Bombardelli and S. Varosanec, “Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1869–1877, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S.-R. Hwang, K.-L. Tseng, and K.-C. Hsu, “Hermite-Hadamard type and Fejér type inequalities for general weights (I),” Journal of Inequalities and Applications, vol. 2013, article no. 170, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. B. Micherda and T. Rajba, “On some hermite-hadamard-Fejér inequalities for (k,h)-convex functions,” Journal of Inequalities and Applications, vol. 15, no. 4, Article ID 15-79, pp. 931–940, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Park, “Inequalities of hermite-hadamard-Fejer type for convex functions via fractional integrals,” International Journal of Mathematical Analysis, vol. 8, no. 59, pp. 2927–2937, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Z. Sarikaya, “On new Hermite Hadamard-Fejér type integral inequalities,” Studia. Universitatis Babes-Bolyai Math, vol. 57, no. 3, pp. 377–386, 2012. View at Google Scholar · View at MathSciNet
  7. K.-L. Tseng, G.-S. Yang, and K.-C. Hsu, “Some inequalities for differentiable mappings and applications to Fejér inequality and weighted trapezoidal formula,” Taiwanese Journal of Mathematics, vol. 15, no. 4, pp. 1737–1747, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. G.-S. Yang and K.-L. Tseng, “Inequalities of Hadamard's type for Lipschitzian mappings,” Journal of Mathematical Analysis and Applications, vol. 260, no. 1, pp. 230–238, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Eshaghi Gordji, M. Rostamian Delavar, and M. De La Sen, “On φ-convex functions,” Journal of Mathematical Inequalities, vol. 10, no. 1, pp. 173–183, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  10. M. Eshaghi Gordji, S. S. Dragomir, and M. Rostamian Delavar, “An inequality related to -convex functions (II),” International Journal of Nonlinear Analysis and Applications, vol. 6, no. 2, pp. 26–32, 2016. View at Google Scholar
  11. M. R. Delavar and S. S. Dragomir, “On η-Convexity,” Journal of Inequalities and Applications, vol. 20, no. 1, pp. 203–216, 2017. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Rostamian Delavar and M. De La Sen, “Some generalizations of Hermite–Hadamard type inequalities,” SpringerPlus, vol. 5, no. 1, article no. 1661, 2016. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Rostamian Delavar and M. De La Sen, “On generalization of Fejér type inequalities,” Communications in Mathematics and Applications, vol. 8, no. 1, pp. 31–43, 2017. View at Google Scholar
  14. P. Cerone and S. S. Dragomir, “Trapezoidal-type rules from an inequalities point of view,” in Handbook of Analytic-Computational Methods in Applied Mathematics, G. Anastassiou, Ed., pp. 65–134, CRC Press, New York, NY, USA, 2000. View at Google Scholar · View at MathSciNet
  15. P. Cerone and S. S. Dragomir, “Midpoint-type rules from an inequalities point of view,” in Handbook of Analytic-Computational Methods in Applied Mathematics, G. A. Anastassiou, Ed., pp. 135–200, CRC Press, New York, NY, USA, 2000. View at Google Scholar · View at MathSciNet
  16. P. Cerone and S. S. Dragomir, “New bounds for the three-point rule involving the Riemann-Stieltjes integral,” in Advances in Statistics, Combinatorics and Related Areas, C. Gulati, Ed., pp. 53–62, World Science Publishing, 2002. View at Google Scholar · View at MathSciNet
  17. S. S. Dragomir and R. P. Agarwal, “Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula,” Applied Mathematics Letters, vol. 11, no. 5, pp. 91–95, 1998. View at Publisher · View at Google Scholar · View at Scopus
  18. U. g. Kirmaci, “Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,” Applied Mathematics and Computation, vol. 147, no. 1, pp. 137–146, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus