Research Article

The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions

Volume: 5 Number: 2 March 30, 2017
EN

The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions

Abstract

 Recently, in [5], with a new approach, the authors obtained a new fractional Hermite-Hadamard type inequality for convex functions by using only the left Riemann-Liouville fractional integral. They also had new equalities to have new fractional trapezoid and midpoint type inequalities for convex functions, In this papers, we will use the same equalities to have new fractional trapezoid and  midpoint type inequalities for quasi-convex functions. Our results generalise the study [3].

Keywords

References

  1. J. Hadamard, ´Etude sur les propri´et´es des fonctions enti`eres et en particulier d’une fonction consid´er´ee par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
  2. Ch. Hermite, Sur deux limites d’une int´egrale d´efinie, Mathesis, 3 (1883), 82–83.
  3. D.A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of the University of Craiova, Math. Comp. Sci. Ser., 34 (2007): 82-87.
  4. U. S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 147 (2004) 137-146.
  5. M. Kunt, D. Karapınar, S. Turhan, ˙I. ˙Is¸can, The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for convex functions, RGMIA Research Report Collection, 20 (2017), Article 101, 8 pp.
  6. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
  7. Y. Zhou, Basic theory of fractional differential equations, World Scientific, New Jersey (2014).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Dunya Karapinar * This is me
Türkiye

Mehmet Kunt
Türkiye

Publication Date

March 30, 2017

Submission Date

July 10, 2017

Acceptance Date

August 9, 2017

Published in Issue

Year 1970 Volume: 5 Number: 2

APA
Karapinar, D., & Kunt, M. (2017). The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions. New Trends in Mathematical Sciences, 5(2), 222-228. https://izlik.org/JA26JW95MA
AMA
1.Karapinar D, Kunt M. The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions. New Trends in Mathematical Sciences. 2017;5(2):222-228. https://izlik.org/JA26JW95MA
Chicago
Karapinar, Dunya, and Mehmet Kunt. 2017. “The Left Rieaman-Liouville Fractional Hermite-Hadamard Type Inequalities for Quasi-Convex Functions”. New Trends in Mathematical Sciences 5 (2): 222-28. https://izlik.org/JA26JW95MA.
EndNote
Karapinar D, Kunt M (March 1, 2017) The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions. New Trends in Mathematical Sciences 5 2 222–228.
IEEE
[1]D. Karapinar and M. Kunt, “The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 222–228, Mar. 2017, [Online]. Available: https://izlik.org/JA26JW95MA
ISNAD
Karapinar, Dunya - Kunt, Mehmet. “The Left Rieaman-Liouville Fractional Hermite-Hadamard Type Inequalities for Quasi-Convex Functions”. New Trends in Mathematical Sciences 5/2 (March 1, 2017): 222-228. https://izlik.org/JA26JW95MA.
JAMA
1.Karapinar D, Kunt M. The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions. New Trends in Mathematical Sciences. 2017;5:222–228.
MLA
Karapinar, Dunya, and Mehmet Kunt. “The Left Rieaman-Liouville Fractional Hermite-Hadamard Type Inequalities for Quasi-Convex Functions”. New Trends in Mathematical Sciences, vol. 5, no. 2, Mar. 2017, pp. 222-8, https://izlik.org/JA26JW95MA.
Vancouver
1.Dunya Karapinar, Mehmet Kunt. The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for quasi-convex functions. New Trends in Mathematical Sciences [Internet]. 2017 Mar. 1;5(2):222-8. Available from: https://izlik.org/JA26JW95MA