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
MEHMET Kunt
,
İMDAT İşcan
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
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- [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.
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- [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
MEHMET Kunt
,
İMDAT İşcan
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.