Some Different Type Integral Inequalities and Their Applications

Abstract

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized-m-\(((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))\)-convex mappings. Secondly, an identity pertaining twice differentiable mappings defined on m-invex set is used. By using the notion of generalized-m-\(((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))\)-convexity 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. At the end, some applications to special means for different positive real numbers are provided as well.