Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus

Abstract

In this paper, we establish several new (p,q)-integral identities involving (p,q)-integrals by using the definition of a (p,q)-derivative. These results are then used to derive (p,q)-integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.

Keywords

• Simpson inequality
• Newton inequality
• convex function
• (<i>p</i>,<i>q</i>)-derivative
• (<i>p</i>,<i>q</i>)-integral
• (<i>p</i>,<i>q</i>)-calculus