DIFFERENCE DOUBLE SEQUENCES OF BI-COMPLEX NUMBERS

In this article, we have introduced the notion of convergence of difference double sequences in Pringsheim’s sense, difference null in Pringsheim’s sense, bounded difference, bounded convergence differ ence, bounded null difference, regular convergence difference and reg ular null difference double sequences of bi-complex numbers. We have proved that these are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, we have established their differ ent algebraic and topological properties, as well as some of their geo metric properties. Suitable examples have been discussed to support the introduction of these classes of sequences and during the investi gation of their properties for failure cases.