Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2018, 6(4), 125-128
DOI: 10.12691/tjant-6-4-5
Open AccessArticle

On New Trapezoid Type Inequalities for h-convex Functions via Generalized Fractional Integral

P. O. MOHAMMED1,

1Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq

Pub. Date: August 28, 2018

Cite this paper:
P. O. MOHAMMED. On New Trapezoid Type Inequalities for h-convex Functions via Generalized Fractional Integral. Turkish Journal of Analysis and Number Theory. 2018; 6(4):125-128. doi: 10.12691/tjant-6-4-5

Abstract

In this paper, some new inequalities of the trapezoid type for h-convex functions via generalized fractional integral are given. The results also provide new estimates on these types of trapezoid inequalities for Riemann-Liouville type fractional operators.

Keywords:
Riemann-Liouville fractional integral h-convex function Convex functions integral inequalities

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References:

[1]  M. Z. Sarikaya and F. Ertugral, On the generalized Hermite-Hadamard inequalities, (2017), submitted.
 
[2]  S. Mubeen and G. M Habibullah, k-Fractional integrals and application, Int. J. Contemp. Math. Sciences, 7(2) (2012), 89-94.
 
[3]  F. Ertugral and M. Z. Sarikaya, Some Trapezoid type inequalities for generalized fractional integral, (2018), submitted.
 
[4]  M. Tomar, E. Set and M. Z. Sarᵻkaya, Hermite-Hadamard type Riemann-Liouville fractional integral inequalities for convex functions, AIP Conference Proceedings 1726, 020035 (2016).
 
[5]  H. Kavurmaci, M. Avci and M. E. Ozdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, J. Inequal. Appl., 2011, 2011:86, 11 pp.
 
[6]  S. Erden and M. Z. Sarikaya, New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications, Moroccan J. Pure and Appl. Anal.(MJPAA), 2(2) (2016), 107-117.
 
[7]  P. Burai and A. Hazy, On approximately h-convex functions, J. Convex Anal., 18(2) (2011), 447-454.
 
[8]  M. Z. Sarᵻkaya, A. Sağlam and H. Yildirim, On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2 (2008) 335-341.
 
[9]  M. Z. Sarᵻkaya, E. Set and M. E. Özdemir, On some new inequalities of Hadamard type involving h-convex functions, Acta Math. Univ. Comenian. (N.S.), 79(2) (2010), 265-272.
 
[10]  M. Tunç, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27:4 (2013), 559-565.