STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE

Abstract

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.