Author:
Alp Necmettin,Sarikaya Mehmet Zeki
Abstract
AbstractThe aim of this work is to obtain quantum estimates for q-Hardy type integral inequalities on quantum calculus. For this, we establish new identities including quantum derivatives and quantum numbers. After that, we prove a generalized q-Minkowski integral inequality. Finally, with the help of the obtained equalities and the generalized q-Minkowski integral inequality, we obtain the results we want. The outcomes presented in this paper are q-extensions and q-generalizations of the comparable results in the literature on inequalities. Additionally, by taking the limit $q\rightarrow 1^{-}$
q
→
1
−
, our results give classical results on the Hardy inequality.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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