Our aim in this article is to incorporate the notion of “strongly s-convex function” and prove a new integral identity. Some new inequalities of Simpson type for strongly s-convex function utilizing integral identity and Holder’s inequality are considered.

In this paper, we establish some new inequalities of Simpson’s type based on ( α , m ) -convexity for differentiable mappings. This contributes to new better estimates than presented already. Some applications for special means of real numbers and error estimates for some numerical quadrature rules are also given.

In this paper, we derive general integral identity by establishing new Hermite-Hadamard type inequalities for functions whose absolute values of derivatives are convex and concave. Cor- responding error estimates for midpoint formula are also included. Moreover, some applications to special means of real numbers are also provided.