In this paper, we prove two identities involving quantum derivatives,
quantum integrals, and certain parameters. Using the newly proved
identities, we prove new inequalities of Simpson's and Newton's type for
quantum differentiable convex functions under certain assumptions.
Moreover, we discuss the special cases of our main results and obtain
some new and existing Simpson's type inequalities, Newton's type
inequalities, midpoint type inequalities and trapezoidal type
inequalities.