On sequence space derived by the domain of q-Cesàro matrix in ℓ space and the associated operator ideal

Sequence spaces derived by the triple band generalized Fibonacci difference operator

“…Recently, several authors constructed interesting Banach sequence spaces using the domain of special triangles, for instance İlkhan [26], İlkhan and Kara [24], Roopaei [54,55], Roopaei et al [53], and Yaying et al [64]. We followed this approach and introduced BK spaces k (F(B)) and ∞ (F(B)) defined as the domain of the product matrix F (B(x, y, z)) in the spaces k and ∞ , respectively.…”

“…The set X is a sequence space and is known as the domain of matrix in the space X. Additionally, if X is BK -space and is a triangle, then X is also BK -space endowed with the norm s X = s X [27], where the matrix = (ψ rv ) is called a triangle if ψ rr = 0 for all r ∈ N and ψ rv = 0 for v > r. Using this famous result several authors [4,29,35,41,48] in the literature constructed new BK -spaces. We also mention [22,23,26,[53][54][55][62][63][64] for some recent publications and textbooks [6,47,61] in this field.…”

Map Ideal of Type the Domain of r -Cesàro Matrix in the Variable Exponent ℓ t

“…Makarov and Faried [11] examined that for each infinite dimensional Banach space P , Q and r > b > 0, then B α ℓ b ðP , QÞÞB α ℓ r ðP , QÞUBðP , QÞ. Yaying et al [12] defined and examined the sequence space, χ t r , whose r-Cesàro matrix is in ℓ t , with r ∈ ð0, 1 and 1 ≤ t…”

“…(1) When r = 1 and t l = t, with l ∈ N, then ces ðtÞ r is compressed to ces t , introduced and studied by Ng and Lee [26]. Different types of Cesàro summable sequence spaces of nonabsolute type have been studied by many authors [27][28][29][30][31] (2) If t l = t, with l ∈ N, ces ðtÞ r is truncated to χ t r studied by Yaying et al [12] The goal of this paper is efficient like so in Section 2 we offer the sufficient setting on any linear space of sequences V , and we mark it a private sequence space (pss), so as to the class B s V constructs a map ideal. We apply this theorem on ces ðtÞ r .…”

Kannan Contraction Operator on the Domain of r . -Cesàro Matrix in ℓ<

“…Makarov and Faried [5] proved that for every infinite dimensional Banach spaces P , Q, and r > b > 0, hence B α ℓ b ðP , QÞÞB α ℓ r ðP , QÞUBðP , QÞ. Yaying et al [6] constructed the sequence space, χ t r , whose its r-Cesàro matrix in ℓ t , with r ∈ ð0, 1 and 1 ≤ t≤∞. They studied the quasi Banach ideal of type χ t r , with r ∈ ð0, 1 and 1 < t<∞.…”