Some <i>q</i>-Symmetric Integral Inequalities Involving <i>s</i>-Convex Functions

Abstract

The q-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.

Keywords

• quantum calculus
• q-symmetric quantum calculus
• Ostrowski-type inequalities
• Hermite–Hadamard-type inequalities