WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
A New $$\mathbb{D}$$-Normed Banach Bicomplex $$\mathbb{BC}$$-Module Derived Using Matrix of Hyperbolic Fibonacci Numbers
Authors: ,
Abstract: In this paper, we present a new matrix $$ \tilde{F} = \left ( \tilde{F}_{nm} \right )_{n,m=1}^{∞}$$ consisting hyperbolic Fibonacci numbers. Also, we construct new $$\mathbb{D}$$-normed Banach bicomplex $$\mathbb{BC}$$-modules $$ l_{p}^{k}\left ( \mathbb{BC}, \tilde{F} \right )$$ and $$ l_{∞}^{k}\left ( \mathbb{BC}, \tilde{F} \right )$$ using this matrix. Moreover, we demonstrate that these new $$\mathbb{BC}$$-modules are isometrically isomorphic to $$ l_{p}^{k}\left ( \mathbb{BC}\right )$$ and $$ l_{∞}^{k}\left ( \mathbb{BC}\right )$$, respectively. We further study some inclusion theorems for this new type.
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Keywords: Bicomplex number, sequence space, hyperbolic Fibonacci number, inclusion relation, $$\mathbb{BC}$$-linearity,
bicomplex $$\mathbb{BC}$$-module
Pages: 203-208
DOI: 10.37394/23206.2025.24.20