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Title: Variations around a general quantum operator
Authors: Cardoso, José Luís dos Santos
Keywords: General quantum difference operator
β-Lebesgue spaces
Jackson q-Integral
Issue Date: 17-Feb-2020
Publisher: Springer
Citation: Cardoso, J.L. Variations around a general quantum operator. Ramanujan J 54, 555–569 (2021).
Abstract: Let I ⊆ R be an interval and β : I → I a strictly increasing and continuous function with a unique fixed point s0 ∈ I that satisfies (s0 − t)(β(t) − t) ≥ 0 for all t ∈ I, where the equality holds only when t = s0. For appropriate choices of the function β, the quantum operator defined by Hamza et al., Dβ[ f ](t) := f β(t) − f (t) β(t) − t if t = s0 and Dβ[ f ](s0) := f (s0) if t = s0, generalizes both the Jackson q-operator Dq and the Hahn (quantum derivative) operator, Dq,ω. With respect to the inverse of this general quantum difference operator, the β-integral, we study properties of the corresponding Lebesgue spaces L p β ([a, b]).
Peer Reviewed: yes
Document Type: Article
Appears in Collections:DMAT - Artigo publicado em Revista Científica Indexada

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