On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field

Abstract EN

The studies on sequence spaces were extended by using the notion of associated multiplier sequences.

A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces.

In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction.

Sometimes the associated multiplier sequence delays the rate of convergence of a sequence.

In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are ⋆-complete.

By using the notion of multiplier sequence, the α-, β-, and γ-duals of certain paranormed spaces have been computed and their basis has been constructed.