Some normed binomial difference sequence spaces related to the [Formula: see text] spaces.

ABSTRACT

The aim of this paper is to introduce the normed binomial sequence spaces [Formula see text] by combining the binomial transformation and difference operator, where [Formula see text]. We prove that these spaces are linearly isomorphic to the spaces [Formula see text] and [Formula see text], respectively. Furthermore, we compute Schauder bases and the α-, ß- and γ-duals of these sequence spaces.