Research Article

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

Volume: 5 Number: 1 April 3, 2017
EN

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

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.

Keywords

References

  1. [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. [2] I. Işcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  3. [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. [4] i. İşcan,, Hermite-Hadamard type inequalities for harmonically $(\alpha,m)$-convex functions, Hacet. J. Math. Stat., 45 (2) (2016), 381-390.
  5. [5] i. İşcan,, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  6. [6] i. İşcan,, A new generalization of some integral inequalities for $(\alpha,m)$-convex functions, Mathematical Sciences, 7 (22) (2013) 1-8.
  7. [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. [8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

MEHMET Kunt
Karadeniz Technical University, Science Faculty, Department of Mathematics,61080, Trabzon
Türkiye

İMDAT İşcan This is me
Giresun University, Science and Arts Faculty, Department of Mathematics, Giresun
Türkiye

Publication Date

April 3, 2017

Submission Date

April 3, 2017

Acceptance Date

December 25, 2016

Published in Issue

Year 2017 Volume: 5 Number: 1

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. https://izlik.org/JA29MP56NG
AMA
1.Kunt M, İşcan İ. HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. 2017;5(1):201-213. https://izlik.org/JA29MP56NG
Chicago
Kunt, MEHMET, and İMDAT İşcan. 2017. “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 5 (1): 201-13. https://izlik.org/JA29MP56NG.
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
[1]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, Apr. 2017, [Online]. Available: https://izlik.org/JA29MP56NG
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 1, 2017): 201-213. https://izlik.org/JA29MP56NG.
JAMA
1.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, Apr. 2017, pp. 201-13, https://izlik.org/JA29MP56NG.
Vancouver
1.MEHMET Kunt, İMDAT İşcan. HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. [Internet]. 2017 Apr. 1;5(1):201-13. Available from: https://izlik.org/JA29MP56NG
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