Almost convergence and Euler totient matrix

Demiriz, Serkan; İlkhan, Merve; Kara, Emrah Evren

doi:10.1007/s43034-019-00041-0

Cited by 16 publications

(7 citation statements)

References 23 publications

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“…For relevant literature, we refer to the papers [10][11][12][13][14][15] and textbooks [16][17][18]. For some recent publications dealing with the domain of triangles in classical spaces, we refer [19][20][21][22][23][24][25][26][27][28].…”

Section: Notations and Definitions On ðP Qþ-calculusmentioning

confidence: 99%

On Generalized $(p, q)$ -Euler Matrix and Associated Sequence Spaces

Yaying¹,

Hazarika

Mursaleen

2021

Journal of Function Spaces

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In this study, we introduce new BK -spaces b s r , t p , q and b ∞ r , t p , q derived by the domain of p , q -analogue B r , t p , q of the binomial matrix in the spaces ℓ s and ℓ ∞ , respectively. We study certain topological properties and inclusion relations of these spaces. We obtain a basis for the space b s r , t p , q and obtain Köthe-Toeplitz duals of the spaces b s r , t p , q and b ∞ r , t p , q . We characterize certain classes of matrix mappings from the spaces b s r , t p , q and b ∞ r , t p , q to space μ ∈ ℓ ∞ , c , c 0 , ℓ 1 , b s , c s , c s 0 . Finally, we investigate certain geometric properties of the space b s r , t p , q .

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Section: Notations and Definitions On ðP Qþ-calculusmentioning

confidence: 99%

On Generalized $(p, q)$ -Euler Matrix and Associated Sequence Spaces

Yaying¹,

Hazarika

Mursaleen

2021

Journal of Function Spaces

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“…It is a known fact that a convergent sequence is almost convergent such that its ordinary and generalized limits are equal. See the papers [2][3][4][5][6][7][8][9][10][11][12][13][14] for more on almost convergence and Banach limit.…”

Section: Introductionmentioning

confidence: 99%

Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences

İlkhan

ÖRNEK>

2022

Mathematical Sciences and Applications E-Notes

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“…The spaces are

ℓ_{p} (Φ) = \{u = (u_{n}) \in ω : \sum_{n} {|\frac{1}{n} \sum_{k | n} φ (k) u_{k}|}^{p} < \infty\} (1 \leq p < \infty)

and

ℓ_{\infty} (Φ) = \{u = (u_{n}) \in ω : \sup_{n} |\frac{1}{n} \sum_{k | n} φ (k) u_{k}| < \infty\} .

In a recent paper by İlkhan, 4 matrix domains of the matrix Φ in the spaces c and c 0 have been introduced. By using the domains of some special summability matrices, several new spaces have been introduced by Sarıgöl, 5 Et, 6 Et and Çolak, 7 Altay et al, 8 Altay and Başar, 9 Kirişçi and Başar, 10 Mursaleen, 11 Mursaleen and Noman, 12,13 Demiriz and Çakan, 14 Kara, 15 Kara and İlkhan, 16 Candan, 17,18 Kirişçi, 19 Başarır and Kara, 20,21 Meng and Mei, 22 Das and Hazarika, 23 Yaying and Hazarika, 24 İlkhan et al, 25 Zengin Alp and İlkhan, 26 İlkhan, 27 Erdem and Demiriz, 28 and Demiriz et al 29 …”

Section: Introductionmentioning

confidence: 99%