On some new integral inequalities concerning twice differentiable generalized relative semi-(m,h)-preinvex mappins

Abstract

The authors first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-$(m,h)$-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-$(m,h)$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via conformable fractional integrals are established. These new presented inequalities are also applied to construct inequalities for special means.