New Parameterized Inequalities for <i>η</i>-Quasiconvex Functions via (<i>p</i>, <i>q</i>)-Calculus

Abstract

In this work, first, we consider novel parameterized identities for the left and right part of the (p,q)-analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized (p,q)-trapezoid and parameterized (p,q)-midpoint type integral inequalities via η-quasiconvex function. By changing values of parameter μ∈[0,1], some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the η-quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained.

Keywords

• quantum calculus
• post quantum calculus
• parameterized (<i>p</i>, <i>q</i>)-estimates for midpoint and trapezoidal type inequalities
• <i>η</i>-quasiconvexity