Research
A Survey on Developments in Sequence Spaces and Introduction to Bicomplex Duals
A survey on recent developments in the duality theory of sequence spaces has been done and duality in some Bicomplex sequence spaces is introduced which gives rise to sixteen types of different duals.
On Some Bicomplex Modules
A class of entire bicomplex sequences denoted by B, studied by Srivastava & Srivastava in 2007 is studied and is shown to be a bicomplex module. The subclasses of this class,studied by Wagh in 2008, are also shown to be bicomplex modules. Further they have been shown to form module structure over the class B.
On Certain Bicomplex Duals
We investigated certain bicomplex duals of the class of bicomplex sequences defined by Srivastava & Srivastava [S2] and of the subclasses defined by Nigam [N1] and Wagh [W2]. Köthe & Toeplitz duals for bicomplex sequence spaces, defined and studied in [W3], have been extended further. Two types of duals namely αβ- dual and βα- dual have been defined and relations between these duals and the duals of classes defined by [S2] and subclasses defined by [W2] have been established. Relation between these duals and the i2 – conjugate of a bicomplex number is also studied.
