Weaker Conditions for the <i>q</i>-Steffensen Inequality and Some Related Generalizations

Abstract

The aim of this paper is to study the q-Steffensen inequality and to prove some weaker conditions for this inequality in quantum calculus. Further, we prove q-analogues of some frequently used generalizations of Steffensen’s inequality and obtain some refinements of q-Steffensen’s inequality and its generalizations.

Keywords

• Steffensen’s inequality
• <i>q</i>-integral
• weaker conditions
• generalizations
• refinements