Newton and Simpson Formula Type Inequalities Via Generalized Convexity in Quantum Calculus

Abstract

In this proposal, we will establish a novel form of Newton’s and Simpson’s inequalities in quantum calculus by using (a; m)-convexity. Newly obtained inequalities may be con- verted into Simpson and Newton inequalities in quantum for generalized convex functions by using q1-integral. Thus, these developments allow us to develop new bounds for quantum integral inequalities. In this research work we will present some new results by employing quantum calculus for differentiable functions and we will also give some new applications along with some new definitions. For the development of these new quantum integral inequalities, we will use Holder and Power mean integral inequalities by using quantum calculus. The discoveries of numerous authors in quantum and classical calculus were broadened and expanded in this paper. Hence, these new results will lead us to generalization of prior results.