PARANORMED RIESZ DIFFERENCE SEQUENCE SPACES OF FRACTIONAL ORDER

In this article we introduce paranormed Riesz difference sequence spaces of fractional order alpha, r(0)(t) (p, Delta((alpha))), r(c)(t)(p, Delta((alpha))) and r(infinity)(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 Riesz mean matrix R-t. We give some topological properties, obtain the Schauder basis and determine the alpha-,beta- and gamma- duals of the new spaces. Finally, we characterize certain matrix classes related to these new spaces.