k-fractional integral trapezium-like inequalities through [Formula: see text]-convex and [Formula: see text]-convex mappings

Hao Wang; Tingsong Du; Yao Zhang

doi:10.1186/s13660-017-1586-6

k-fractional integral trapezium-like inequalities through [Formula: see text]-convex and [Formula: see text]-convex mappings

J Inequal Appl. 2017;2017(1):311. doi: 10.1186/s13660-017-1586-6. Epub 2017 Dec 19.

Authors

Hao Wang¹, Tingsong Du¹, Yao Zhang¹

Affiliation

¹ Department of Mathematics, College of Science, China Three Gorges University, Yichang, 443002 China.

Abstract

In this paper, a new general identity for differentiable mappings via k-fractional integrals is derived. By using the concept of [Formula: see text]-convexity, [Formula: see text]-convexity and the obtained equation, some new trapezium-like integral inequalities are established. The results presented provide extensions of those given in earlier works.

Keywords: [Formula: see text]-convex functions; k-fractional integrals.