In this work using the generalized difference operator ∆m, we generalize the sequence space m (φ)... more In this work using the generalized difference operator ∆m, we generalize the sequence space m (φ) to sequence space m (φ, p, β) (∆m), give some topological properties about this space and show that the space m (φ, p, β) (∆m) is a BK−space by a suitable norm. The results obtained generalizes some known results.
In this paper the concepts of Δmv -statistical convergence of order ɑ and strong (p, Δmv )-Cesàro... more In this paper the concepts of Δmv -statistical convergence of order ɑ and strong (p, Δmv )-Cesàro summability of order ɑ are introduced for sequences of complex (or real) numbers. Some relations between the Δmv -statistical convergence of order and strong (p, Δmv )-Ces`aro summability of order ɑ are given. Also some relations between the space ωɑp (Δmv, ƒ) and Sɑ (Δmv ) are examined.Keywords: Sequences, statistical convergence, Cesàro summability.
We determine the relations between the classes S^λ of almost λ-statistically convergent sequences... more We determine the relations between the classes S^λ of almost λ-statistically convergent sequences and the relations between the classes V^,λ of strongly almost V,λ-summable sequences for various sequences λ, μ in the class Λ. Furthermore we also give the relations between the classes S^λ of almost λ-statistically convergent sequences and the classes V^,λ of strongly almost V,λ-summable sequences for various sequences λ,μ∈Λ.
We intend to make a new approach and introduce the concepts of statistical convergence of order a... more We intend to make a new approach and introduce the concepts of statistical convergence of order and strongly -Cesàro summability of order for double sequences of complex or real numbers. Also, some relations between the statistical convergence of order and strong -Cesàro summability of order are given.
The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Becau... more The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Because this sequences are just the sequences x=(xk)=(k) and x=(xk)=1 respectively and any term of these sequences can not be 0. In this short not we give Example 3* and Example 4* to show that the inclusions given in Theorem 2.4
A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergen... more A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergent double sequence into a convergent sequence with the same limit. Firstly, Robison [GM Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926) 50–73] presented the necessary and sufficient conditions for regular matrix transformations of double sequences. In this paper, the conditions of Robison are extended to the class of regular matrix transformations between the double sequence spaces c2PB ( ...
In this work using the generalized difference operator ∆m, we generalize the sequence space m (φ)... more In this work using the generalized difference operator ∆m, we generalize the sequence space m (φ) to sequence space m (φ, p, β) (∆m), give some topological properties about this space and show that the space m (φ, p, β) (∆m) is a BK−space by a suitable norm. The results obtained generalizes some known results.
In this paper the concepts of Δmv -statistical convergence of order ɑ and strong (p, Δmv )-Cesàro... more In this paper the concepts of Δmv -statistical convergence of order ɑ and strong (p, Δmv )-Cesàro summability of order ɑ are introduced for sequences of complex (or real) numbers. Some relations between the Δmv -statistical convergence of order and strong (p, Δmv )-Ces`aro summability of order ɑ are given. Also some relations between the space ωɑp (Δmv, ƒ) and Sɑ (Δmv ) are examined.Keywords: Sequences, statistical convergence, Cesàro summability.
We determine the relations between the classes S^λ of almost λ-statistically convergent sequences... more We determine the relations between the classes S^λ of almost λ-statistically convergent sequences and the relations between the classes V^,λ of strongly almost V,λ-summable sequences for various sequences λ, μ in the class Λ. Furthermore we also give the relations between the classes S^λ of almost λ-statistically convergent sequences and the classes V^,λ of strongly almost V,λ-summable sequences for various sequences λ,μ∈Λ.
We intend to make a new approach and introduce the concepts of statistical convergence of order a... more We intend to make a new approach and introduce the concepts of statistical convergence of order and strongly -Cesàro summability of order for double sequences of complex or real numbers. Also, some relations between the statistical convergence of order and strong -Cesàro summability of order are given.
The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Becau... more The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Because this sequences are just the sequences x=(xk)=(k) and x=(xk)=1 respectively and any term of these sequences can not be 0. In this short not we give Example 3* and Example 4* to show that the inclusions given in Theorem 2.4
A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergen... more A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergent double sequence into a convergent sequence with the same limit. Firstly, Robison [GM Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926) 50–73] presented the necessary and sufficient conditions for regular matrix transformations of double sequences. In this paper, the conditions of Robison are extended to the class of regular matrix transformations between the double sequence spaces c2PB ( ...
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