Some new $k$-fractional trapezium-like integral inequalities via generalized relative semi-$(r;m,h_{1},h_{2})$-preinvex mappings and applications

A. Kashuri, M. Adil Khan, R. Liko

In this article, we first presented a new general identity concerning differentiable mappings defined on $m$-invex set via $k$-fractional integrals. By using the concept of generalized relative semi-$(r;m,h_{1},h_{2})$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to trapezium-like integral inequalities via $k$-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article. Applications to special means for trapezium-like integral inequalities via $k$-fractional integrals are provided as well. 

Tbilisi Mathematical Journal, Vol. 12(3) (2019), pp. 1-19