The authors develop an R(p,q)-topological analysis framework including deformed Gamma functions, Banach and Frechet spaces, and analogues of Cauchy-Hadamard, Borel-Caratheodory, and Phragmen-Lindelof theorems for holomorphic functions.
On the fundamental theorem of $(p,q)$-calculus and some $(p,q)$-Taylor formulas
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abstract
In this paper, the $(p,q)$-derivative and the $(p,q)$-integration are investigated. Two suitable polynomials bases for the $(p,q)$-derivative are provided and various properties of these bases are given. As application, two $(p,q)$-Taylor formulas for polynomials are given, the fundamental theorem of $(p,q)$-calculus is included and the formula of $(p,q)$-integration by part is proved.
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2026 1verdicts
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Topological analysis in $\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\mathcal{R}(p,q)-$quantum deformed algebra
The authors develop an R(p,q)-topological analysis framework including deformed Gamma functions, Banach and Frechet spaces, and analogues of Cauchy-Hadamard, Borel-Caratheodory, and Phragmen-Lindelof theorems for holomorphic functions.