Fibonacci Difference Research Articles

Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space

The forthcoming property of this manuscript is its calculating of the goal of norms and lower bounds of matrix operators taken from the weighted sequence space ℓp(w) onto a novel one defined in the present article as the generalized Fibonacci weighted difference sequence space. In this process, first of all the Fibonacci difference matrix F˜(r,s) and the space composed of sequences of which F˜(r,s)-transforms lie in ℓp(w˜), where r,s∈R are defined. Additionaly, since the seminormed space ℓp(w˜,F˜(r,s)) has the absolute homogeneous property, the topological characteristics on it are distributed symmetrically everywhere in the space.

SPACES OF FIBONACCI DIFFERENCE IDEAL CONVERGENT SEQUENCES IN RANDOM 2–NORMED SPACE

In this article, by using Fibonacci difference matrix F and the notion of ideal convergence of sequences in random 2–normed space, we introduce some new spaces of Fibonacci difference ideal convergent sequences with respect to random 2 -norm and study some inclusion relations, topological and algebraic properties of these spaces.

On generalized Fibonacci difference sequence spaces and compact operators

In this paper, we introduce Fibonacci backward difference operator [Formula: see text] of fractional order l by the composition of Fibonacci band matrix [Formula: see text] and difference operator [Formula: see text] of fractional order l, defined by [Formula: see text] and introduce sequence spaces [Formula: see text] and [Formula: see text] We present some topological properties, obtain Schauder basis and determine [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the spaces [Formula: see text] and [Formula: see text] We characterize certain classes of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to any of the space [Formula: see text] [Formula: see text] [Formula: see text] or [Formula: see text] Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces [Formula: see text] and [Formula: see text]

On Λ-Fibonacci difference sequence spaces of fractional order

In this article, we introduce -Fibonacci difference operator of fractional order which is obtained by the composition of -Fibonacci matrix and backward fractional difference operator defined by and introduce the sequence spaces and We give some topological properties, and obtain the Schauder basis of the new spaces.

Sequence spaces derived by the triple band generalized Fibonacci difference operator

In this article we introduce the generalized Fibonacci difference operator mathsf{F}(mathsf{B}) by the composition of a Fibonacci band matrix F and a triple band matrix mathsf{B}(x,y,z) and study the spaces ell _{k}( mathsf{F}(mathsf{B})) and ell _{infty }(mathsf{F}(mathsf{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})) and ell _{infty }(mathsf{F}(mathsf{B})) to space mathsf{Y}in {ell _{infty },c_{0},c,ell _{1},cs_{0},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})) and ell _{infty }(mathsf{F}(mathsf{B})) to mathsf{Y}in { ell _{infty }, c, c_{0}, ell _{1},cs_{0},cs,bs} using the Hausdorff measure of non-compactness.

Two dimensional second order Fibonacci summation formula with extorial functions

This paper aims to obtain the extorial type solutions for Fibonacci difference equations on real valued function defined in two dimensional space having shift value ℓ. Using two dimensional second order Fibonacci nabla difference operator and its inverse, we derived Second order fibonacci summation formula of product of real valued polynomial. A function obtained by replacing polynomial into polynomial factorials in the expansion of exponential function is called extorial function. Using extorial functions defined in ℝ2, we obtain solution of certain type of two dimensional second order difference equations. Suitable examples and numerical verifications are given to validate the findings.

Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces

Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F̂ and ideal convergence defined the notion of c_{0}^{I}(hat{F}), c^{I}(hat{F}) and l_{infty }^{I}(hat{F}). In this paper, we give the ideal convergence of Fibonacci difference sequence space in intuitionistic fuzzy normed space with respect to fuzzy norm (mu ,nu ). Moreover, we investigate some basic properties of the said spaces such as linearity, hausdorffness.

Higher Order Fibonacci Summation Formula with Extorial Functions

This paper aims to obtain extorial type solutions of Fibonacci difference equations having shift value. A higher order Fibonacci summation formula of product of polynomial and extorial functions is obtained by higher order Fibonacci nabla difference operator, its inverse and the higher order Fibonacci numbers. Extorial function is a function obtained by replacing polynomial into polynomial factorials in the exponential function. Suitable examples with numerical verification are inserted to illustrate our main results.

Discrete Heat Equation model of Rod by Partial Fibonacci Difference Operator with shift values

Partial Fibonacci difference equation is introduced and subjected to investigation in discrete heat equation by having recourse to Fibonacci difference operator with shift values in this paper. By having Fourier law of cooling as its basis, the heat transfer in the long rod is investigated and the solutions obtained are validated by MATLAB.

Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space

Norm of an operator T:X→Y is the best possible value of U satisfying the inequality urn:x-wiley:mma:media:mma5244:mma5244-math-0001 and lower bound for T is the value of L satisfying the inequality urn:x-wiley:mma:media:mma5244:mma5244-math-0002 where ‖.‖X and ‖.‖Y are the norms on the spaces X and Y, respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space ℓp(w) into a new space called as Fibonacci weighted difference sequence space. For this purpose, we firstly introduce the Fibonacci difference matrix and the space consisting of sequences whose ‐transforms are in .

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

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.

On ideal convergence Fibonacci difference sequence spaces

The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the Fibonacci difference matrix F̂ by using the Fibonacci sequence (f_{n}) for nin{{0, 1, ldots}} and introduced new sequence spaces related to the matrix domain of F̂. In this paper, by using the Fibonacci difference matrix F̂ defined by the Fibonacci sequence and the notion of ideal convergence, we introduce the Fibonacci difference sequence spaces c^{I}_{0}(hat {F}), c^{I}(hat{F}), and ell^{I}_{infty}(hat{F}). Further, we study some inclusion relations concerning these spaces. In addition, we discuss some properties on these spaces such as monotonicity and solidity.

Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

Some new Fibonacci difference spaces of non-absolute type and compact operators

In this paper, we introduce the spaces and which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the duals of those spaces and also construct their bases. We also characterize some matrix classes on the spaces and Here we characterize the subclasses of compact operators where and by applying the Hausdorff measure of non-compactness.

Some properties of generalized Fibonacci sequence spaces

In this paper, we define new spaces as a generalization of the Fibonacci difference sequence spaces. Also, we establish some inclusion theorems related to these spaces and find the -, -, -duals. Lastly, we characterize some matrix classes on these spaces.

On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core

In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space . Also, we show that the spaces and are linearly isomorphic. Further, we determine the -dual of the space and characterize some matrix classses on this space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.

Compact operators on some Fibonacci difference sequence spaces

In this paper, we characterize the matrix classes $(\ell _{1},\ell _{p}(\widehat{F}))$ ( $1\leq p<\infty $ ), where $\ell _{p}(\widehat{F})$ 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.

Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers

In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces ℓp(F) and ℓ∞(F) to be compact, where 1 ≤p < ∞.

Products of [formula omitted] matrices related to non autonomous Fibonacci difference equations

A technique to compute arbitrary products of a class of Fibonacci 2×2 square matrices is proved in this work. General explicit solutions for non autonomous Fibonacci difference equations are obtained from these products. In the periodic non autonomous Fibonacci difference equations the monodromy matrix, the Floquet multipliers and the Binet’s formulas are obtained. In the periodic case explicit solutions are obtained and the solutions are analyzed.

Some families of zero- error block codes for the two-user binary adder channel with feedback

Families of zero-error codes for the real binary adder channel with feedback that achieve high rate pairs are introduced. Two families of zero-error block codes are given for the case in which only one of the two senders receives feedback about the channel output. In the first of these families, the uninformed sender transmits at a rate of nearly one bit per symbol and the informed sender transmits slightly less that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</tex> bit per symbol. The second family is designed for the case in which the informed sender sends at or near one bit per symbol and the uninformed one sends nearly <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</tex> bit per symbol. A family of zero-error codes is introduced, based on the Fibonacci recursion; these codes are readily implemented by means of a simple square-dividing strategy. The Fibonacci codes achieve <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{1}=R_{2}=\log_{2} [(1 + \sqrt{5})/2]</tex> in the limit of large block length. Time-sharing between members of these three code families is used to obtain an achievable rate region, or inner bound, to the zero-error capacity region for block coding. For the case in which the feedback is available to both senders, a variant of the Fibonacci difference equation is used to generate zero-error block codes with slightly higher asymptotic rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{1}=R_{2}=0.717</tex> .