Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus

Abstract

In this paper, using the notions of qκ2-quantum integral and qκ2-quantum derivative, we present some new identities that enable us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors.

Keywords

• Simpson’s inequalities
• Newton’s inequalities
• quantum calculus
• convex functions