Some new sequence spaces derived by the domain of the triple band matrix

Euler-Ces`aro difference spaces of bounded, convergent and null sequences

“…∆ c 0 , c and ℓ ∞ c 0 (∆), c(∆) and ℓ ∞ (∆) [16] R t c 0 , c and ℓ ∞ r t 0 , r t c and r t ∞ [17,28] B (r, s) c 0 , c and ℓ ∞ c 0 , c and ℓ ∞ [18] B (r, s, t ) c 0 , c and ℓ ∞ c 0 (B ), c(B ) and ℓ ∞ (B ) [19] C 1 c 0 , c and ℓ ∞ c 0 , c and X ∞ [27,26] A r c 0 and c a r 0 and a r c [29] E r c 0 , c and ℓ ∞ e r 0 , e r c and e r ∞ [31,30] ∆ 2 c 0 and c c 0 (∆ 2 ) and c(∆ 2 ) [32] u∆ 2 c 0 and c c 0 (u; ∆ 2 ) and c(u; ∆ 2 ) [33] ∆ m c 0 and c c 0 (∆ m ) and c(∆ m ) [34,35] R q c 0 and c (N , q) 0 and (N , q) [36] ∆ (m) c 0 and c c 0 (∆ (m) ) and c(∆ (m) ) [37] G(u, v) c 0 , c and ℓ ∞ c 0 (u, v), c(u, v) and ℓ ∞ (u, v) [38] Λ c 0 and c c λ 0 and c λ [39] B ( r , s) c 0 , c and ℓ ∞ c 0 , c and ℓ ∞ [40] A λ c 0 and c A λ (c 0 ) and A λ (c) [41] F c 0 and c c 0 ( F ) and c( F ) [42] N t c 0 , c and ℓ ∞ c 0 (N t ), c(N t ) and X a(p) [43,44] In 1978, the domain of Cesàro matrix C 1 of order one in the classical sequence spaces ℓ ∞ and ℓ p were introduced by Ng and Lee [26], where 1 ≤ p < ∞. Following Ng and Lee [26], Sengönül and Başar [27] have studied the domain of Cesàro matrix C 1 of order one in the classical sequence spaces c 0 and c. In 1978, the domain of Nörlund matrix N t in the classical sequence spaces ℓ ∞ and ℓ p were introduced by Wang [44], where 1 ≤ p < ∞.…”

“…where X denotes any of the spaces ℓ ∞ , c, c 0 and ℓ p with 1 ≤ p < ∞, and B (r, s)x = (sx k−1 +r x k ) with r, s ∈ R \ {0}. Following Kirişçi and Başar [4], Sönmez [19] have been examined the sequence space X (B ) as the set of all sequences whose B (r, s, t )-transforms are in the space…”

Almost convergence and generalized weighted mean

“…[7]; and Başar and Kirişçi [2]; Kayaduman andŞengönül [5]; Sönmez [10,11] and Candan [3] are recent works on the domain of certain triangle matrices in the spaces f 0 , f and in the classical sequence spaces, the present paper is their natural continuation.…”

Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers

“…where u = (u k ) is an arbitrary fixed sequence and 0 < p k ≤ H < ∞ for all k ∈ N. Also in [11,13,14,18,24,25,27,28,36,38], authors studied some difference sequence spaces. Let S X denote the unit sphere in a normed linear space X.…”