Affiliation:
1. Department of Mathematics , Faculty of Sciences , Ondokuz Mayıs University , Samsun , Türkiye
Abstract
Abstract
In this work, it is assumed that the norm over bicomplex numbers is the
hyperbolic (
𝔻
{\mathbb{D}}
-valued) norm. In this paper, we provide an overview
of bicomplex Lebesgue spaces and investigate some of their geometric
properties, including
𝔹
ℂ
{\mathbb{B}\mathbb{C}}
-convexity,
𝔹
ℂ
{\mathbb{B}\mathbb{C}}
-strict convexity, and
𝔹
ℂ
{\mathbb{B}\mathbb{C}}
-uniform convexity. Moreover, the basic inequalities such as
𝔻
{\mathbb{D}}
-Hölder’s inequality and
𝔻
{\mathbb{D}}
-Minkowski inequality for bicomplex
Lebesgue spaces are presented, used to show geometric properties.
Cited by
1 articles.
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