ON THE SPACES OF FIBONACCI DIFFERENCE ABSOLUTELY p-SUMMABLE, NULL AND CONVERGENT SEQUENCES

Başarır, Metin; Başar, Feyzı; Kara, Emrah Evren

doi:10.5644/sjm.12.2.04

Cited by 21 publications

(21 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Kara defined the Fibonacci difference matrix

\overset{F}{true} = false({\overset{f}{true}}_{n k} false)

{\hat{f}}_{n k} = \{\begin{matrix} - \frac{f_{n + 1}}{f_{n}}, & k = n - 1 \\ \frac{f_{n}}{f_{n + 1}}, & k = n \\ 0, & 0 \leq k < n - 1 or k > n \end{matrix}

and introduced some new difference sequence spaces by using this matrix. For more applications of Fibonacci numbers in sequence spaces, one can see previous works …”

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

View full text Add to dashboard Cite

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).

show abstract

“…Kara defined the Fibonacci difference matrix

\overset{F}{true} = false({\overset{f}{true}}_{n k} false)

{\hat{f}}_{n k} = \{\begin{matrix} - \frac{f_{n + 1}}{f_{n}}, & k = n - 1 \\ \frac{f_{n}}{f_{n + 1}}, & k = n \\ 0, & 0 \leq k < n - 1 or k > n \end{matrix}

and introduced some new difference sequence spaces by using this matrix. For more applications of Fibonacci numbers in sequence spaces, one can see previous works …”

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%

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

İlkhan

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Karakaş [8], Fibonacci sayılarından oluşan bir Toeplitz matrisi kullanarak klasik dizi uzaylarının cebirsel ve topolojik özelliklerini vermiştir. Başarır ve diğerleri [9], Fibonacci dizisiyle oluşturulan bir matris yardımıyla     Çalışmanın asıl amacı, Lucas sayıları yardımıyla regüler bir matris oluşturmak ve bu matrisin tanım bölgesini kullanarak yeni bir dizi uzayı elde ederek, bu uzayın klasik dizi uzaylarıyla olan ilişkisini incelemektir.…”

Section: Leonardounclassified

An Application On The Lucas Numbers And Infinite Toeplitz Matrices

Karakaş¹,

Karabudak²

2017

Cumhuriyet Science Journal

View full text Add to dashboard Cite

“…Fibonacci sequence have may applications in science, art and architecture. In recent years, due to the interesting structure of the Fibonacci sequence, it has been found some application in the theory of summability and sequence spaces ( [2], [6], [3], [4], [13]). For example; M. Karakaş in [12] by considering the Fibonacci matrix as follows:…”

Section: Introductionmentioning

confidence: 99%