q-Hardy type inequalities for quantum integrals

Abstract The aim of this work is to obtain quantum estimates for q -Hardy type integral inequalities on calculus. For this, we establish new identities including derivatives and numbers. After that, prove a generalized -Minkowski inequality. Finally, with the help obtained equalities inequality, results want. outcomes presented in paper are -extensions -generalizations comparable literature inequalities. Additionally, by taking limit $q\rightarrow 1^{-}$ q → 1 − , our give classical Hardy