Some new k-Riemann-Liouville fractional integral inequalities associated with the strongly η-quasiconvex functions with modulus [Formula: see text]

Eze R Nwaeze; Seth Kermausuor; Ana M Tameru

doi:10.1186/s13660-018-1736-5

Some new k-Riemann-Liouville fractional integral inequalities associated with the strongly η-quasiconvex functions with modulus $μ \geq 0$

J Inequal Appl. 2018;2018(1):139. doi: 10.1186/s13660-018-1736-5. Epub 2018 Jun 20.

Authors

Eze R Nwaeze¹, Seth Kermausuor², Ana M Tameru¹

Affiliations

¹ 1Department of Mathematics, Tuskegee University, Tuskegee, USA.
² 2Department of Mathematics and Computer Science, Alabama State University, Montgomery, USA.

Abstract

A new class of quasiconvexity called strongly η-quasiconvex function was introduced in (Awan et al. in Filomat 31(18):5783-5790, 2017). In this paper, we obtain some new k-Riemann-Liouville fractional integral inequalities associated with this class of functions. For specific values of the associated parameters, we recover results due to Dragomir and Pearce (Bull. Aust. Math. Soc. 57:377-385, 1998), Ion (Ann. Univ. Craiova, Math. Sci. Ser. 34:82-87, 2007), and Alomari et al. (RGMIA Res. Rep. Collect. 12(Supplement):Article ID 14, 2009).

Keywords: Hermite–Hadamard inequality; Riemann–Liouville fractional integrals; Strongly η-quasiconvex.