Research Article

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

Volume: 4 Number: 3 September 30, 2016
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

References

  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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mustafa Aydin This is me
Türkiye

Kerim Bekar This is me
Türkiye

Publication Date

September 30, 2016

Submission Date

February 6, 2016

Acceptance Date

March 28, 2016

Published in Issue

Year 2016 Volume: 4 Number: 3

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, and 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 (September 1, 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, and K. Bekar, “On generalization of different type inequalities for (α,m)-convex functions via fractional integrals”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 49–57, Sept. 2016, [Online]. Available: 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 (September 1, 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, et al. “On Generalization of Different Type Inequalities for (α,m)-Convex Functions via Fractional Integrals”. New Trends in Mathematical Sciences, vol. 4, no. 3, Sept. 2016, pp. 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]. 2016 Sep. 1;4(3):49-57. Available from: https://izlik.org/JA34KA99AZ