Taylor theory associated with Hahn difference operator

In this paper, we establish Taylor theory based on Hahn’s difference operator D q , ω which is defined by D q , ω f ( t ) = f ( q t + ω ) − f ( t ) t ( q − 1 ) + ω , t ≠ ω 1 − q , where q ∈ ( 0 , 1 ) and ω is a positive number.

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Bibliographic Details
Published in:Journal of inequalities and applications 2020-05, Vol.2020 (1), p.1-19, Article 124
Main Authors: Oraby, Karima, Hamza, Alaa
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Finite differences
Hahn difference operator D q , ω $D_{q,\omega}
Mathematics
Mathematics and Statistics
Operators (mathematics)
Taylor series
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Description
Summary:In this paper, we establish Taylor theory based on Hahn’s difference operator D q , ω which is defined by D q , ω f ( t ) = f ( q t + ω ) − f ( t ) t ( q − 1 ) + ω , t ≠ ω 1 − q , where q ∈ ( 0 , 1 ) and ω is a positive number.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02392-y