Araştırma Makalesi

On generalization of different type inequalities for (α,m)-convex functions via fractional integrals

Cilt: 4 Sayı: 3 30 Eylül 2016
PDF İndir
EN

On generalization of different type inequalities for (α,m)-convex functions via fractional integrals

Abstract


 In this paper, new identity for fractional integrals have been defined. By using of this identity, the authors obtained new general inequalities containing all of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are -convex via Riemann Liouville fractional integral.


Keywords

Kaynakça

  1. M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
  2. M.K. Bakula, M.E. Ozdemir and J. Pecaric, Hadamard type inequalities for m-convex and (α,m)-convex functions, J. Inequal. Pure Appl. Math. 9(4) (2008) Article 96, p. 12. [Online: http://jipam.vu.edu.au/article.php?sid=1032].
  3. R. Gorenflo and F. Mainardi,Fractional calculus, integral and differential equations of fractional order, Springer Verlag, Wien, 1997, 223-276.
  4. I. Iscan, A new generalization of some integral inequalities for (α,m)-convex functions, Mathematical Sciences 7(22) (2013)1-8.
  5. I. Iscan, New estimates on generalization of some integral inequalities for (α,m)-convex functions, Contemp. Anal. Appl. Math. 1(2) (2013), 253-264 .
  6. I. Iscan, Hermite-Hadamard type inequalities for functions whose derivatives are (α,m)-convex, International Journal of Engineering and Applied sciences 2(3) (2013), 69-78.
  7. V.G. Miheşan, A generalization of the convexity. Seminer on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania, 1993.
  8. S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, USA, 1993.

Ayrıntılar

Birincil Dil

İngilizce

Konular

-

Bölüm

Araştırma Makalesi

Yazarlar

Mustafa Aydin Bu kişi benim
Türkiye

Kerim Bekar Bu kişi benim
Türkiye

Yayımlanma Tarihi

30 Eylül 2016

Gönderilme Tarihi

6 Şubat 2016

Kabul Tarihi

28 Mart 2016

Yayımlandığı Sayı

Yıl 2016 Cilt: 4 Sayı: 3

Kaynak Göster

APA
Iscan, İ., Aydin, M., & Bekar, K. (2016). On generalization of different type inequalities for (α,m)-convex functions via fractional integrals. New Trends in Mathematical Sciences, 4(3), 49-57. https://izlik.org/JA34KA99AZ
AMA
1.Iscan İ, Aydin M, Bekar K. On generalization of different type inequalities for (α,m)-convex functions via fractional integrals. New Trends in Mathematical Sciences. 2016;4(3):49-57. https://izlik.org/JA34KA99AZ
Chicago
Iscan, İmdat, Mustafa Aydin, ve Kerim Bekar. 2016. “On generalization of different type inequalities for (α,m)-convex functions via fractional integrals”. New Trends in Mathematical Sciences 4 (3): 49-57. https://izlik.org/JA34KA99AZ.
EndNote
Iscan İ, Aydin M, Bekar K (01 Eylül 2016) On generalization of different type inequalities for (α,m)-convex functions via fractional integrals. New Trends in Mathematical Sciences 4 3 49–57.
IEEE
[1]İ. Iscan, M. Aydin, ve K. Bekar, “On generalization of different type inequalities for (α,m)-convex functions via fractional integrals”, New Trends in Mathematical Sciences, c. 4, sy 3, ss. 49–57, Eyl. 2016, [çevrimiçi]. Erişim adresi: https://izlik.org/JA34KA99AZ
ISNAD
Iscan, İmdat - Aydin, Mustafa - Bekar, Kerim. “On generalization of different type inequalities for (α,m)-convex functions via fractional integrals”. New Trends in Mathematical Sciences 4/3 (01 Eylül 2016): 49-57. https://izlik.org/JA34KA99AZ.
JAMA
1.Iscan İ, Aydin M, Bekar K. On generalization of different type inequalities for (α,m)-convex functions via fractional integrals. New Trends in Mathematical Sciences. 2016;4:49–57.
MLA
Iscan, İmdat, vd. “On generalization of different type inequalities for (α,m)-convex functions via fractional integrals”. New Trends in Mathematical Sciences, c. 4, sy 3, Eylül 2016, ss. 49-57, https://izlik.org/JA34KA99AZ.
Vancouver
1.İmdat Iscan, Mustafa Aydin, Kerim Bekar. On generalization of different type inequalities for (α,m)-convex functions via fractional integrals. New Trends in Mathematical Sciences [Internet]. 01 Eylül 2016;4(3):49-57. Erişim adresi: https://izlik.org/JA34KA99AZ