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HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS

Year 2017, Volume: 5 Issue: 1, 201 - 213, 03.04.2017

Abstract

In this paper, we establish some fractional Hermite-Hadamard type inequalities for harmonically $(\alpha,m)$-convex functions. Also, we give some applications to special means of positive real numbers by using obtained inequalities.

References

  • [1] M. K. Bakula, M. E.  Ozdemir, J. Pecaric, Hadamard type inequalities for m-convex and $(\alpha,m)$-convex functions, J. Inequal. Pure Appl. Math., 9 (4), Article 96, p. 12, 2008.
  • [2] I. Işcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  • [3] i. İşcan, New estimates on generalization of some integral inequalities for $(\alpha,m)$-convex functions, Contemp. Anal. Appl. Math., 1 (2) (2013) 253-264.
  • [4] i. İşcan,, Hermite-Hadamard type inequalities for harmonically $(\alpha,m)$-convex functions, Hacet. J. Math. Stat., 45 (2) (2016), 381-390.
  • [5] i. İşcan,, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  • [6] i. İşcan,, A new generalization of some integral inequalities for $(\alpha,m)$-convex functions, Mathematical Sciences, 7 (22) (2013) 1-8.
  • [7] i. İşcan,, Hermite-Hadamard type inequalities for functions whose derivatives are $(\alpha,m)$-convex, Int. J. Eng. Appl. Sci., 2 (3) (2013) 69-78.
  • [8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [9] V. G. Mihasen, A generalization of the convexity, Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania, 1993.
  • [10] M. E.  Ozdemir, H. Kavurmacı, E. Set, Ostorowski's type inequalities for $(\alpha,m)$-convex functions, Kyungpook Math. J., 50 (2010) 371-378.
  • [11] E. Set, M. E.  Ozdemir, S. S. Dragomir, On Hadamard-type inequalities involving several kinds of convexity, J. Inequal. Appl. 2010 (2010) 12, http://dx.doi.org/10.1155/2010/286845 (Article ID 286845).
  • [12] J. Wang, C. Zho, Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013 (325) (2013) 15pp.
Year 2017, Volume: 5 Issue: 1, 201 - 213, 03.04.2017

Abstract

References

  • [1] M. K. Bakula, M. E.  Ozdemir, J. Pecaric, Hadamard type inequalities for m-convex and $(\alpha,m)$-convex functions, J. Inequal. Pure Appl. Math., 9 (4), Article 96, p. 12, 2008.
  • [2] I. Işcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  • [3] i. İşcan, New estimates on generalization of some integral inequalities for $(\alpha,m)$-convex functions, Contemp. Anal. Appl. Math., 1 (2) (2013) 253-264.
  • [4] i. İşcan,, Hermite-Hadamard type inequalities for harmonically $(\alpha,m)$-convex functions, Hacet. J. Math. Stat., 45 (2) (2016), 381-390.
  • [5] i. İşcan,, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  • [6] i. İşcan,, A new generalization of some integral inequalities for $(\alpha,m)$-convex functions, Mathematical Sciences, 7 (22) (2013) 1-8.
  • [7] i. İşcan,, Hermite-Hadamard type inequalities for functions whose derivatives are $(\alpha,m)$-convex, Int. J. Eng. Appl. Sci., 2 (3) (2013) 69-78.
  • [8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [9] V. G. Mihasen, A generalization of the convexity, Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania, 1993.
  • [10] M. E.  Ozdemir, H. Kavurmacı, E. Set, Ostorowski's type inequalities for $(\alpha,m)$-convex functions, Kyungpook Math. J., 50 (2010) 371-378.
  • [11] E. Set, M. E.  Ozdemir, S. S. Dragomir, On Hadamard-type inequalities involving several kinds of convexity, J. Inequal. Appl. 2010 (2010) 12, http://dx.doi.org/10.1155/2010/286845 (Article ID 286845).
  • [12] J. Wang, C. Zho, Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013 (325) (2013) 15pp.
There are 12 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

MEHMET Kunt

İMDAT İşcan This is me

Publication Date April 3, 2017
Submission Date April 3, 2017
Acceptance Date December 25, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Kunt, M., & İşcan, İ. (2017). HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 5(1), 201-213.
AMA Kunt M, İşcan İ. HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. April 2017;5(1):201-213.
Chicago Kunt, MEHMET, and İMDAT İşcan. “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 201-13.
EndNote Kunt M, İşcan İ (April 1, 2017) HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 5 1 201–213.
IEEE M. Kunt and İ. İşcan, “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 5, no. 1, pp. 201–213, 2017.
ISNAD Kunt, MEHMET - İşcan, İMDAT. “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 5/1 (April 2017), 201-213.
JAMA Kunt M, İşcan İ. HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. 2017;5:201–213.
MLA Kunt, MEHMET and İMDAT İşcan. “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 201-13.
Vancouver Kunt M, İşcan İ. HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. 2017;5(1):201-13.
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