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.
Highlights
Italian mathematician Leonardo Fibonacci found the Fibonacci number sequence
The Fibonacci sequence originated from a rabbit problem in his first book “Liber Abaci”
The Golden Ratio, which is known outside the academic community, is used in many fields of science
Summary
The Fibonacci sequence originated from a rabbit problem in his first book “Liber Abaci”. This sequence is used in many fields. C, c0 and∞ are called as sequences space convergent, convergent to zero and bounded, respectively. Let λ be a sequence space and K be an infinite matrix. Many sequence spaces have been recently defined in this way. The α-, β- and γ-duals Pα , P β and Pγ of a sequence spaces P are defined, respectively, as. The α-, β- and γ-duals of the spaces bs( F ) and cs( F ) are found and some matrix tranformations of them are given
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