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In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm|⋅|{|\cdot|_{\Bbbk}}and we discuss some topological and geometric concepts such as completeness, convexity, strict convexity and uniform convexity in the bicomplex setting with respect to the hyperbolic-valued norm∥⋅∥,⋅{\|\cdot\|_{\mathbb{D},\cdot}}by defining the concept of{\mathbb{D}}-normed Banach bicomplex  A -module and constructing{\mathbb{D}}-normed Banach bicomplex⁢ℂ{\mathbb{BC}}-moduleslp⁢(⁢ℂ){l_{p}^{\Bbbk}(\mathbb{BC})}.

On bicomplex 𝔹ℂ-modules l p 𝕜 (𝔹ℂ) and some of their geometric properties