Some different type integral inequalities concerning twice differentiable generalized relative semi-(r;m,h)-preinvex mappings

A. Kashuri, R. Liko

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-(r;m,h)-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on m-invex set is derived. By using the notion of generalized relative semi-(r;m,h)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article. 

Tbilisi Mathematical Journal, Vol. 11(1) (2018), pp. 79-97