An Application On The Lucas Numbers And Infinite Toeplitz Matrices

Karakaş, Murat; Karabudak, Hasan

doi:10.17776/csj.340510

Cited by 16 publications

(19 citation statements)

References 9 publications

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“…As an application of Fibonacci numbers into infinite regular matrices, Kara and Başarır have defined a new regular matrix F = ( f n k ) by using the Fibonacci numbers as follows:

f_{n k} = \{\begin{matrix} \frac{f_{k}^{2}}{f_{n} f_{n + 1}}, & 1 \leq k \leq n \\ 0, & k > n . \end{matrix}

(For the characterization of a regular matrix, one can see lemma 2.2 in Kovac). Also, Kara and Başarır have defined some new spaces as the matrix domain of F in some classical sequence spaces.…”

Section: Introductionmentioning

confidence: 99%

“…For more applications of Fibonacci numbers in sequence spaces, one can see previous works. [9][10][11][12][13][14][15][16][17][18][19][20] As an application of Fibonacci numbers into infinite regular matrices, Kara and Başarır 21 have defined a new regular matrix F = (f nk ) by using the Fibonacci numbers as follows:…”

Section: Introductionmentioning

confidence: 99%

“…(For the characterization of a regular matrix, one can see lemma 2.2 in Kovac 22 ). Also, Kara and Başarır 21 have defined some new spaces as the matrix domain of F in some classical sequence spaces. Recently, by using this matrix, Talebi and Dehghan 23 have introduced the space of Fibonacci weighted sequence space F w,p consisting of all sequences whose…”

Section: Introductionmentioning

confidence: 99%

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

İlkhan

2018

Math Methods in App Sciences

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Norm of an operator T:X→Y is the best possible value of U satisfying the inequality ‖Txfalse‖Y≤U‖xfalse‖X, and lower bound for T is the value of L satisfying the inequality ‖Txfalse‖Y≥L‖xfalse‖X, 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 trueF˜ and the space consisting of sequences whose trueF˜‐transforms are in ℓpfalse(truew˜false).

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“…As an application of Fibonacci numbers into infinite regular matrices, Kara and Başarır have defined a new regular matrix F = ( f n k ) by using the Fibonacci numbers as follows:

f_{n k} = \{\begin{matrix} \frac{f_{k}^{2}}{f_{n} f_{n + 1}}, & 1 \leq k \leq n \\ 0, & k > n . \end{matrix}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

İlkhan

2018

Math Methods in App Sciences

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show abstract

“…The main purpose of the present section, following [5][6][7][8][9][10][11], is to introduce the Fibonacci weighted sequence space F w, p and is to derive some inclusion relations Downloaded by [New York University] at 09:37 25 July 2015 Linear and Multilinear Algebra 3 concerning this space. The Fibonacci weighted sequence space is defined as below:…”

Section: The Fibonacci Weighted Sequence Spaces F W Pmentioning

confidence: 99%

Approximation of upper bound for matrix operators on the Fibonacci weighted sequence spaces

Talebi

Dehghan

2015

Linear and Multilinear Algebra

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“…Theorem 1.1 extends [15], Theorem 3.8, from the Fibonacci sequence space to the domains of invertible summability matrices in p . To see this, consider the Fibonacci sequence space F p defined in [7]:…”

Section: Theorem 11 Suppose Thatmentioning

confidence: 99%