STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE

In this paper, we study some basic properties of bicomplex numbers. We introduce two different types of partial order relations on bicomplex numbers, discuss bicomplex valued metric spaces with respect to two different partial orders, and compare them. We also define a hyperbolic valued metric space...

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Bibliographic Details
Published in:Ural mathematical journal 2023-07, Vol.9 (1), p.49
Main Authors: Bera, Subhajit, Tripathy, Binod Chandra
Format: Article
Language:English
Subjects:
partial order, bi-complex valued metric space, statistically convergent
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Summary:In this paper, we study some basic properties of bicomplex numbers. We introduce two different types of partial order relations on bicomplex numbers, discuss bicomplex valued metric spaces with respect to two different partial orders, and compare them. We also define a hyperbolic valued metric space, the density of natural numbers, the statistical convergence, and the statistical Cauchy property of a sequence of bicomplex numbers and investigate some properties  in a bicomplex metric space and prove that a bicomplex metric space is complete if and only if two complex metric spaces are complete.
ISSN:2414-3952
2414-3952
DOI:10.15826/umj.2023.1.004