Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2017, Cilt: 5 Sayı: 1, 201 - 213, 03.04.2017

Öz

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.

Kaynakça

  • [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.
Yıl 2017, Cilt: 5 Sayı: 1, 201 - 213, 03.04.2017

Öz

Kaynakça

  • [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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

MEHMET Kunt

İMDAT İşcan Bu kişi benim

Yayımlanma Tarihi 3 Nisan 2017
Gönderilme Tarihi 3 Nisan 2017
Kabul Tarihi 25 Aralık 2016
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 1

Kaynak Göster

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. Nisan 2017;5(1):201-213.
Chicago Kunt, MEHMET, ve İMDAT İşcan. “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 5, sy. 1 (Nisan 2017): 201-13.
EndNote Kunt M, İşcan İ (01 Nisan 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 ve İ. İşcan, “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”, Konuralp J. Math., c. 5, sy. 1, ss. 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 (Nisan 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 ve İMDAT İşcan. “HERMITE-HADAMARD TYPE INEQUALITIES FOR HARMONICALLY $(\alpha,m)$-CONVEX FUNCTIONS BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, c. 5, sy. 1, 2017, ss. 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.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.