JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERALIZATION OF INEQUALITIES ANALOGOUS TO HERMITE-HADAMARD INEQUALITY VIA FRACTIONAL INTEGRALS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GENERALIZATION OF INEQUALITIES ANALOGOUS TO HERMITE-HADAMARD INEQUALITY VIA FRACTIONAL INTEGRALS
Iqbal, Muhammad; Iqbal Bhatti, Muhammad; Nazeer, Kiran;
  PDF(new window)
 Abstract
Some Hermite-Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].
 Keywords
Hermite-Hadamard's inequality;convex functions;power-mean inequality;Riemann-Liouville fractional integration;
 Language
English
 Cited by
1.
Properties and Riemann-Liouville fractional Hermite-Hadamard inequalities for the generalized ( α , m ) $(\alpha,m)$ -preinvex functions, Journal of Inequalities and Applications, 2016, 2016, 1  crossref(new windwow)
 References
1.
G. Anastassiou, M. R. Hooshmandasl, A. Ghasemi, and F. Moftakharzadeh, Mont-gomery identities for fractional integrals and related fractional inequalities, J. Inequal. Pure Appl. Math. 10 (2009), no. 4, Article 97, 6 pp.

2.
S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Inequal. Pure Appl. Math. 10 (2009), no. 3, Article 86, 5 pp.

3.
Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 9 (2010), no. 4, 493-497.

4.
Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1 (2010), no. 1, 51-58. crossref(new window)

5.
Z. Dahmani, L. Tabharit, and S. Taf, New generalisations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl. 2 (2010), no. 3, 93-99.

6.
Z. Dahmani, L. Tabharit, and S. Taf, Some fractional integral inequalities, Nonl. Sci. Lett. A 1 (2010), no. 2, 155-160.

7.
S. S. Dragomir, M. I. Bhatti, M. Iqbal, and M. Muddassar, Some new fractional Integral Hermite-Hadamard type inequalities, Journal of Computational Analysis and Application, (Accepted for Publication) (2015).

8.
S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite-Hadamard in- equalities and applications, RGMIA Monographs, Victoria University, 2000; Online: http://www.sta.vu.edu.au/RGMIA/monographs/hermite−hadamard.html.

9.
R. Gorenflo and F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, Fractals and fractional calculus in continuum mechanics (Udine, 1996), 223-276, CISM Courses and Lectures, 378, Springer, Vienna, 1997.

10.
S. Hussain, M. I. Bhatti, and M. Iqbal, Hadamard-type inequalities for s-convex functions I, Punjab Univ. J. Math. 41 (2009), 51-60.

11.
U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (2004), no. 1, 137-146. crossref(new window)

12.
U. S. Kirmaci and M. E. Ozdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 153 (2004), no. 2, 361-368. crossref(new window)

13.
M. Muddassr, M. I. Bhatti, and M. Iqbal, Some New s-Hermite-Hadamard type for differentiable functions and their applications, Proceeding of the Pakistan Academy of Sciences 49 (2012), no. 1, 9-17.

14.
M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. 57 (2013), no. 9-10, 2403-2407. crossref(new window)