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

  • Nilay Değirmen ORCID logo and Birsen Sağır ORCID logo EMAIL logo

Abstract

In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm | | 𝕜 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 , by defining the concept of 𝔻 -normed Banach bicomplex A-module and constructing 𝔻 -normed Banach bicomplex 𝔹 -modules l p 𝕜 ( 𝔹 ) .

Keywords: Bicomplex power
MSC 2010: 46B45; 40A05; 46B20

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Received: 2021-11-24
Revised: 2022-03-10
Accepted: 2022-03-18
Published Online: 2022-10-26
Published in Print: 2023-02-01

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