A New D-Normed Banach Bicomplex BC-Module Derived Using Matrix of Hyperbolic Fibonacci Numbers

Abstract

In this paper, we present a new matrix F∼ = (F∼<inf>nm</inf>)∞<inf>n,m</inf><inf>=1</inf> consisting hyperbolic Fibonacci numbers. Also, we construct new D-normed Banach bicomplex BC-modules l<inf>p</inf>k(BC,F∼) and l<inf>∞</inf>k(BC,F∼) using this matrix. Moreover, we demonstrate that these new BC-modules are isometrically isomorphic to l<inf>p</inf>k (BC) and l<inf>∞</inf>k (BC), respectively. We further study some inclusion theorems for this new type. © 2025 World Scientific and Engineering Academy and Society. All rights reserved.