Statistical convergence of double sequences of bi-complex numbers

Abstract

This article presents the concepts of statistically bounded, statistically bounded convergence, statistically bounded null, statistically regular convergence, statistically regular null double sequences of bi-complex numbers, statistically convergent double sequences in Pringsheim's sense, and statistically null double sequences in Pringsheim's sense. We have established that these spaces are linear, and we have demonstrated their many algebraic, topological, and geometric properties using the Euclidean norm defined on bi-complex numbers. Suitable examples have been discussed.