Some k-fractional extensions of the trapezium inequalities through generalized relative semi-(m,h)-preinvexity

Abstract

In this paper, we first introduce the concept of generalized relative semi-$(m,h)$-preinvex functions, and then a new k-Riemann–Liouville fractional integral identity for differentiable mapping is derived. With the help of this identity, we present some new bounds on trapezium inequalities via generalized relative semi-$(m,h)$-preinvexity. It is pointed out that some new and known special cases can be deduced from main results of the article.

COMMUNICATED BY:

• G. M. N'Guerekata

Keywords:

• Trapezium inequality
• generalized relative semi-$(m,h)$-preinvex functions
• k-Riemann–Liouville fractional integrals

2010 Mathematics Subject Classifications:

• Primary 26A33
• Secondary 26D15
• 26E60
• 41A55

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China under grant no. 61374028.