Calculations in New Sequence Spaces and Application to Statistical Convergence
In this paper we recall recent results that are direct consequences of the fact that (w∞(λ) ,w∞(λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators &am...
Guardado en:
| Autores principales: | , |
|---|---|
| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2010
|
| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300008 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:scielo:S0719-06462010000300008 |
|---|---|
| record_format |
dspace |
| spelling |
oai:scielo:S0719-064620100003000082018-10-08Calculations in New Sequence Spaces and Application to Statistical ConvergenceDE MALAFOSSE,BRUNORAKOČEVIC,VLADIMIR Banach algebra statistical convergence A−statistical convergence infinite matrix In this paper we recall recent results that are direct consequences of the fact that (w∞(λ) ,w∞(λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators Δ, ∑, Δ(λ), or C(λ). Afterwardswe consider the sets [A1,A2]Wτ of all sequences X such that A1 (λ)(|A2(μ) X|) ∈ Wτ where A1 and A2 are of the form C(ξ), C+ (ξ), Δ(ξ), or Δ+ (ξ) and it is given necessary conditions to get |A1 (λ),A2(μ)| Wτ in the form Wξ. Finally we apply the previous results to statistical convergence. So we have conditions to have xk → L(S(A)) where A is either of the infinite matrices D1/τC(λ)C(μ), D1/τΔ(λ)Δ(μ), D1/τΔ(λ)C(μ). We also give conditions to have xk → 0(S(A)) where A is either of the operators D1/τC+ (λ)Δ(μ), D1/τC(λ)C(μ), D1/τC+ (λ)C+(μ), or D1/τΔ(λ)C+(μ).info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.3 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300008en10.4067/S0719-06462010000300008 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Banach algebra statistical convergence A−statistical convergence infinite matrix |
| spellingShingle |
Banach algebra statistical convergence A−statistical convergence infinite matrix DE MALAFOSSE,BRUNO RAKOČEVIC,VLADIMIR Calculations in New Sequence Spaces and Application to Statistical Convergence |
| description |
In this paper we recall recent results that are direct consequences of the fact that (w∞(λ) ,w∞(λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators Δ, ∑, Δ(λ), or C(λ). Afterwardswe consider the sets [A1,A2]Wτ of all sequences X such that A1 (λ)(|A2(μ) X|) ∈ Wτ where A1 and A2 are of the form C(ξ), C+ (ξ), Δ(ξ), or Δ+ (ξ) and it is given necessary conditions to get |A1 (λ),A2(μ)| Wτ in the form Wξ. Finally we apply the previous results to statistical convergence. So we have conditions to have xk → L(S(A)) where A is either of the infinite matrices D1/τC(λ)C(μ), D1/τΔ(λ)Δ(μ), D1/τΔ(λ)C(μ). We also give conditions to have xk → 0(S(A)) where A is either of the operators D1/τC+ (λ)Δ(μ), D1/τC(λ)C(μ), D1/τC+ (λ)C+(μ), or D1/τΔ(λ)C+(μ). |
| author |
DE MALAFOSSE,BRUNO RAKOČEVIC,VLADIMIR |
| author_facet |
DE MALAFOSSE,BRUNO RAKOČEVIC,VLADIMIR |
| author_sort |
DE MALAFOSSE,BRUNO |
| title |
Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_short |
Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_full |
Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_fullStr |
Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_full_unstemmed |
Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_sort |
calculations in new sequence spaces and application to statistical convergence |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2010 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300008 |
| work_keys_str_mv |
AT demalafossebruno calculationsinnewsequencespacesandapplicationtostatisticalconvergence AT rako268evicvladimir calculationsinnewsequencespacesandapplicationtostatisticalconvergence |
| _version_ |
1714206769064968192 |