Abstract:
Some recent results have been found treating the famous Simpson's rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is to address Newton-type integral inequalities by associating with them certain criteria of quantum calculus and the convexity of the functions of various variables. In this article, by using the concept of recently defined q 1 q 2-derivatives and integrals, some of Newton's type inequalities for coordinated convex functions are revealed. We also employ the limits of q 1 , q 2 → 1 − in new results, and attain some new inequalities of Newton's type for coordinated convex functions through ordinary integral. Finally, we provide a thorough application of the newly obtained key outcomes, these new consequences can be useful in the integral approximation study for symmetrical functions, or with some kind of symmetry.