ON THE PARANORMED NORLUND DIFFERENCE SEQUENCE SPACE OF FRACTIONAL ORDER AND GEOMETRIC PROPERTIES

In this article we introduce paranormed Norlund difference sequence space of fractional order alpha, N-t (p, Delta((alpha))) defined by the composition of fractional difference operator Delta((alpha)), defined by (Delta((alpha))x)(k) = Sigma(infinity)(i=0)(-1)(i) Gamma(alpha+1)/i!Gamma(alpha-i+1)x(k-i), and Norlund matrix N-t, We give some topological properties, obtain the Schauder basis and determine the alpha-, beta- and gamma-duals of the new space. We characterize certain matrix classes related to this new space. Finally we investigate certain geometric properties of the space N-t (p, Delta((alpha))). (C) 2021 Mathematical Institute Slovak Academy of Sciences