Paper Title:

Hermite-Hadamard Type Inequalities for k-Riemann Liouville Fractional Integrals Via Two Kinds of Convexity

Author(s):

R. Hussain¹, A. Ali², G. Gulshan³, A. Latif⁴ and K. Rauf⁵

^1,2,3,4Department of Mathematics,
Mirpur University of Science and Technology, Mirpur.
Pakistan.
E-mail¹:  rashida12@gmail.com
E-mail²: unigraz2009@yahoo.com
E-mail³: ghazalagulshan@yahoo.com
E-mail⁴: asialatif87@gmail.com

⁵Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail⁵: krauf@unilorin.edu.ng

Abstract:

In this article, a fundamental integral identity including the first order derivative of a given function via k-Riemann-Liouville fractional integral is established. This is used to obtain further Hermite-Hadamard type inequalities involving left-sided and right-sided k-Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions respectively.