This study uses Raina’s function to obtain a new coordinated $pq$-integral identity. Using this identity, we construct several new $pq$-Simpson’s type inequalities for generalized convex functions on coordinates. Setting $p_1=p_2=1$ in these inequalities yields well-known quantum Simpson’s type inequalities for coordinated generalized convex functions. Our results have important implications for the creation of post quantum mathematical frameworks.

The main focus of this article is to derive some new counterparts to Simpson’s and Newton’s type inequalities involve a class of generalized coordinated convex mappings. This class contains several new and known classes of convexity as special cases. For further demonstration, we deploy the concept of right quantum derivatives to develop two new identities involving Raina’s function. Moreover, by implementing these auxiliary results together with generalized convexity, we acquire a Holder-type inequality. We also acquire some applications of our main findings by making use of suitable substitutions in Raina’s function.