Series spaces derived from absolute Fibonacci summability and matrix transformations

On Certain Series to Series Transformation and Analytic Continuations by Matrix Methods

“…His result was generalized by Schur, who proved that an FF-transform matrix gives convergence preserving transformation iff it is a K-matrix, 1931, Basanquet [3] proved that a matrix of an RF-transformation is convergence preserving iff it is a -matrix ( RF convergence preserving). Vermes further studied the -matrix ( RF convergence preserving) and obtained the result that necessary and sufficient condition for a matrix to give a convergence preserving RRtransformation .Several researchers like Sari ̈ l [4], G ̈kce and Sarig ̈l [4], [6] , Dawson [7] , Borsik et al [8], Borsik [9] and Vermes [14] have studied in the same directions but there results are almost different.Our utmost effort goes on extending P. Vermes [14] works:…”

On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$

“…A double infinite matrix is called factorable if there exist sequences a (1) n , â(1) n , a (2) n , â(2) n such that…”

“…n a (2) m â(1) Corollary 3.3. Let 1 < k < ∞ and A be factorable matrix such that â(1) n , a (1) n , â(2) n , a (2) n ̸ = 0 for all n. Then, A f ⇔ |C , 0, 0| k if and only if Equations (3.1) and (3.2) hold. Theorem 3.4.…”

“…The reason why matrices are used for a general linear operator is that a linear operator from a sequence space to another one can be given by an infinite matrix. In this regard, the literature in the field of summability theory continues to develop not only on the generation of sequence spaces through the matrix domain of a particular matrices such as Hölder, Euler, Ces àro, Hausdorff, Nörlund and weighted mean matrices and on the investigation of their topological, algebraic structures and matrix transformations but also on examinations about new series spaces derived by several absolute summability methods from a different perspective (see, [1][2][3][4][5][6][7][8][9]). Besides of all these, recently, a many of new article using by double series are also placed in literature.…”

Mutlak Cesa ́ro Seri Uzayı Ve Bazı Matris Dönüşümleri

“…In recent times, the literature has grown up concerned with characterizing all matrix operators which transform one given sequence space into another. For example, the absolute Ces𝑎𝑎́ro series space �𝐶𝐶 𝜆𝜆,𝜇𝜇 �(𝑝𝑝) has been introduced and some matrix characterizations of the matrix classes related to the space have been examined in , (see also (Gökçe, 2021;Gökçe and Sarıgöl, 2020;Gökçe and Sarıgöl, 2018;Gökçe and Sarıgöl, 2019a;Güleç, 2020;Sarıgöl, 2016;Zengin and İlkhan, 2019)). In this paper, we investigate the matrix class ��𝐶𝐶 𝜆𝜆,𝜇𝜇 �(𝑝𝑝), Γ� where Γ = {c, 𝑐𝑐 0 , 𝑙𝑙 ∞ }, and then we present some results.…”