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

Abstract

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 star-complete. By using the notion of multiplier sequence, the alpha-, beta-, and gamma-duals of certain paranormed spaces have been computed and their basis has been constructed.