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
Quasi-convex functions Hermite-Hadamard inequality Left Rieaman-Liouville fractional integral
References
- 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.
- Ch. Hermite, Sur deux limites d’une int´egrale d´efinie, Mathesis, 3 (1883), 82–83.
- 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.
- 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.
- 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.
- A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
- Y. Zhou, Basic theory of fractional differential equations, World Scientific, New Jersey (2014).
Abstract
References
- 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.
- Ch. Hermite, Sur deux limites d’une int´egrale d´efinie, Mathesis, 3 (1883), 82–83.
- 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.
- 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.
- 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.
- A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
- Y. Zhou, Basic theory of fractional differential equations, World Scientific, New Jersey (2014).
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | March 30, 2017 |
| Published in Issue | Year 2017 Volume: 5 Issue: 2 |
