Almost Convergent Sequence Space Derived by Generalized Fibonacci Matrix and Fibonacci Core

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

“…Kara defined the Fibonacci difference matrix by 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 …”

“…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:…”

A different approach for almost sequence spaces defined by a generalized weighted means

“…In literature, it was investigated domain of following matrices on the almost convergent and null almost convergent sequence spaces in the sources mentioned: the generalized weighted mean in [4], the double band matrix ( , ) in [5], the Riesz matrix in [6], Cesaro matrix of order 1 in [13], the matrix in [7] can be seen. Further, using generalized difference Fibonacci matrix, Candan and Kayaduman defined ̂ ( , ) space [24]. Furthermore, it can be looked at those works about this topic nearly: [9], [10], [11], [25], [26], [27], [28], [29], [30], [31]…”

“…Lemma 4: i) = ( ) ∈ (ℓ : ) necessary and sufficient condition (15), (22) and (23) yield. [17] ii) = ( ) ∈ ( : ) necessary and sufficient condition (15), (22), (24), and (25) yield. [17] iii) = ( ) ∈ ( : ℓ ) necessary and sufficient condition (19) and (20) yield.…”

A new perspective on paranormed Riesz sequence space of non-absolute type

“…Moreover, the ones who are more interested in the subject are advised to read [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52]. We should note here, there are many different ways to construct new sequence spaces from old ones.…”