Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers

Abstract

In the present paper, we introduce the sequence space lp (F) using a new regular matrix of Fibonacci numbers, where 0 < p < infinity. We investigate its topological properties such as Schauder basis, alpha-, beta- and gamma-duals and its geometric properties like uniformly convex, strictly convex and super-reflexive. We also characterize some matrix classes from the l(p) (F) space to classical sequence spaces.