A new version of ( p , q ) $( p,q ) $ -Hermite–Hadamard’s midpoint and trapezoidal inequalities via special operators in ( p , q ) $( p,q ) $ -calculus

Abstract

Abstract In this paper, we conduct a research on a new version of the ( p , q ) $( p,q ) $ -Hermite–Hadamard inequality for convex functions in the framework of postquantum calculus. Moreover, we derive several estimates for ( p , q ) $(p,q)$ -midpoint and ( p , q ) $(p,q)$ -trapezoidal inequalities for special ( p , q ) $( p,q ) $ -differentiable functions by using the notions of left and right ( p , q ) $(p,q ) $ -derivatives. Our newly obtained inequalities are extensions of some existing inequalities in other studies. Lastly, we consider some mathematical examples for some ( p , q ) $(p,q)$ -functions to confirm the correctness of newly established results.

Keywords

• q-calculus
• ( p , q ) $(p,q)$ -Hermite–Hadamard inequality
• ( p , q ) $(p,q)$ -calculus
• Convex functions