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

Author:

Değirmen Nilay1ORCID,Sağır Birsen1ORCID

Affiliation:

1. Department of Mathematics , Faculty of Art and Sciences , Ondokuz Mayıs University , Samsun , Türkiye

Abstract

Abstract In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm | | 𝕜 {|\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 𝔻 , {\|\cdot\|_{\mathbb{D},\cdot}} by defining the concept of 𝔻 {\mathbb{D}} -normed Banach bicomplex A-module and constructing 𝔻 {\mathbb{D}} -normed Banach bicomplex 𝔹 {\mathbb{BC}} -modules l p 𝕜 ( 𝔹 ) {l_{p}^{\Bbbk}(\mathbb{BC})} .

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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