Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers (original) (raw)

Compact operators on some Fibonacci difference sequence spaces

Journal of Inequalities and Applications, 2015

In this paper, we characterize the matrix classes (1 , p (F)) (1 ≤ p < ∞), where p (F) is some Fibonacci difference sequence spaces. We also obtain estimates for the norms of the bounded linear operators L A defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

On The Spaces of Fibonacci Difference Null and Convergent Sequences

2013

In the present paper, by using the band matrix F defined by the Fibonacci sequence, we introduce the sequence sequence spaces c_0(F) and c(F). Also, we give some inclusion relations and construct the bases of the spaces c_0(F) and c(F). Finally, we compute the alpha-, beta-, gamma-duals of these spaces and characterize the classes (c_0(F),X) and (c(F),X) for certain choice of the sequence space X.

Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers

Afyon Kocatepe University Journal of Sciences and Engineering, 2014

The main purpose of this paper is to introduce the new sequence spaces (F), c(F) and (F) based on the newly defined regular matrix F of Fibonacci numbers. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces.

ON GENERALIZED FIBONACCI DIFFERENCE SPACE DERIVED FROM THE ABSOLUTELY p− SUMMABLE SEQUENCE SPACES

2019

In this study, it is specified \emph{the sequence space} lleft(Fleft(r,sright),pright)l\left( F\left( r,s\right),p\right) lleft(Fleft(r,sright),pright), (where p=left(pkright)p=\left( p_{k}\right) p=left(pkright) is any bounded sequence of positive real numbers) and researched some algebraic and topological features of this space. Further, alpha−,\alpha -,alpha−, beta−,\beta -,beta−, gamma−\gamma -gamma− duals and its Schauder Basis are given. The classes of \emph{matrix transformations} from the space lleft(Fleft(r,sright),pright)l\left( F\left( r,s\right) ,p\right) lleft(Fleft(r,sright),pright) to the spaces linfty,c,l_{\infty },c,linfty,c, and % c_{0} are qualified. Additionally, acquiring qualifications of some other \emph{matrix transformations} from the space lleft(Fleft(r,sright),pright)l\left( F\left( r,s\right) ,p\right) lleft(Fleft(r,sright),pright) to the \emph{Euler, Riesz, difference}, etc., \emph{sequence spaces} is the other result of the paper.

Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

Abstract and Applied Analysis, 2012

We determine the conditions for some matrix transformations fromn(ϕ), where the sequence spacen(ϕ), which is related to theℓpspaces, was introduced by Sargent (1960). We also obtain estimates for the norms of the bounded linear operators defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Advances in Difference Equations, 2020

In this article we introduce the generalized Fibonacci difference operator$\mathsf{F}(\mathsf{B})$F(B)by the composition of a Fibonacci band matrix and a triple band matrix$\mathsf{B}(x,y,z)$B(x,y,z)and study the spaces$\ell _{k}( \mathsf{F}(\mathsf{B}))$ℓk(F(B))and$\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ℓ∞(F(B)). We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces$\ell _{k}(\mathsf{F}(\mathsf{B}))$ℓk(F(B))and$\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ℓ∞(F(B))to space$\mathsf{Y}\in \{\ell _{\infty },c_{0},c,\ell _{1},cs_{0},cs,bs\}$Y∈{ℓ∞,c0,c,ℓ1,cs0,cs,bs}and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces$\ell _{k}(\mathsf{F}(\mathsf{B}))$ℓk(F(B))and$\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ℓ∞(F(B))to$\mathsf{Y}\in \{ \ell _{\infty }, c, c_{0}, \ell _{1},cs_{0},cs,bs\} $Y∈{ℓ∞,c,c0,...

Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Filomat, 2018

In this paper we first introduce N?q?summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c,c0, and l?. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means

Computers & mathematics with applications, 2011

For a sequence x = (x k), we denote the difference sequence by ∆x = (x k − x k−1). Let u = (u k) ∞ k=0 and v = (v k) ∞ k=0 be the sequences of real numbers such that u k ̸ = 0, v k ̸ = 0 for all k ∈ N. The difference sequence spaces of weighted means λ(u, v, ∆) are defined as λ(u, v, ∆) = {x = (x k) : W (x) ∈ λ}, where λ = c, c 0 and ℓ ∞ and the matrix W = (w nk) is defined by w nk =  u n (v k − v k+1); (k < n), u n v n ; (k = n), 0; (k > n). In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on λ(u, v, ∆). Further, we characterize some classes of compact operators on these spaces by using the Hausdorff measure of noncompactness.

On compact operators on the Riesz Bm-difference sequence space

Iranian Journal of Science and Technology (Sciences), 2011

In this paper, we give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz-difference sequence space ,. For this purpose, we apply the Hausdorff measure of noncompactness and use some results.