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Symmetry 2018, 10(7), 274; https://doi.org/10.3390/sym10070274

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

Department of Mathematics, Faculty of Arts and Sciences, Gaziantep University, Gaziantep 27310, Turkey
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Received: 13 June 2018 / Revised: 1 July 2018 / Accepted: 5 July 2018 / Published: 11 July 2018
(This article belongs to the Special Issue Mathematical Physics and Symmetry)
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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,rR\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. View Full-Text
Keywords: Fibonacci numbers; Fibonacci double band matrix; sequence spaces; difference matrix; matrix transformations; α, β, γ-duals Fibonacci numbers; Fibonacci double band matrix; sequence spaces; difference matrix; matrix transformations; α, β, γ-duals
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Yaşar, F.; Kayaduman, K. A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence. Symmetry 2018, 10, 274.

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