Mathematica Eterna
Open Access

Abstract

A New Approach on the Spaces of Generalized Fibonacci Difference Null and Convergent Sequences

Murat Candan

In this current study, the most apparent aspect is to submit new sequence spaces c0(Fb(r, s)) and c(Fb(r, s)) under the domain of the matrix Fb(r, s) constituted by using Fibonacci sequence and non-zero real number r and s, of c0 and c respectively. Here, we have studied some algebraic structures including some inclusion relations, linear isomorphism, solidity and some topological structures such as basis of the spaces c0(Fb(r, s)) and c(Fb(r, s)). Eventually, we have presented the alpha-, beta-, gamma-duals of these spaces using available technique in the literature and characterization of the classes (c0(Fb(r, s)), X) and (c(Fb(r, s)), X) for some sequence space X.