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
- M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
- 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].
- R. Gorenflo and F. Mainardi,Fractional calculus, integral and differential equations of fractional order, Springer Verlag, Wien, 1997, 223-276.
- I. Iscan, A new generalization of some integral inequalities for (α,m)-convex functions, Mathematical Sciences 7(22) (2013)1-8.
- I. Iscan, New estimates on generalization of some integral inequalities for (α,m)-convex functions, Contemp. Anal. Appl. Math. 1(2) (2013), 253-264 .
- 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.
- V.G. Miheşan, A generalization of the convexity. Seminer on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania, 1993.
- 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
İmdat Iscan
*
Türkiye
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