A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence

Abstract

The main topic in this article is to define and examine new sequence spaces bs(F^(s,r)) and cs(F^(s,r))), where F^(s,r) is generalized difference Fibonacci matrix in which s,r∈R\0. Some algebric properties including some inclusion relations, linearly isomorphism and norms defined over them are given. In addition, it is shown that they are Banach spaces. Finally, the α-, β- and γ-duals of the spaces bs(F^(s,r)) and cs(F^(s,r)) are appointed and some matrix transformations of them are given.

Keywords

• Fibonacci numbers
• Fibonacci double band matrix
• sequence spaces
• difference matrix
• matrix transformations
• α, β, γ-duals