Generalized Almost Convergence and Core Theorems of Double Sequences
The idea of [λ, μ]-almost convergence (briefly, F[λ, μ]-convergence) has been recently introduced and studied by Mohiuddine and Alotaibi (2014). In this paper first we define a norm on F[λ, μ] such that it is a Banach space and then we define and characterize those four-dimensional matrices which tr...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/152910 |
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| _version_ | 1849404775764852736 |
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| author | S. A. Mohiuddine Abdullah Alotaibi |
| author_facet | S. A. Mohiuddine Abdullah Alotaibi |
| author_sort | S. A. Mohiuddine |
| collection | DOAJ |
| description | The idea of [λ, μ]-almost convergence (briefly, F[λ, μ]-convergence) has been recently introduced and studied by Mohiuddine and Alotaibi (2014). In this paper first we define a norm on F[λ, μ] such that it is a Banach space and then we define and characterize those four-dimensional matrices which transform F[λ, μ]-convergence of double sequences x=(xjk) into F[λ, μ]-convergence. We also define a F[λ, μ]-core of x=(xjk) and determine a Tauberian condition for core inclusions and core equivalence. |
| format | Article |
| id | doaj-art-9a2eaef416aa413889bd4adaac6ca662 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9a2eaef416aa413889bd4adaac6ca6622025-08-20T03:36:53ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/152910152910Generalized Almost Convergence and Core Theorems of Double SequencesS. A. Mohiuddine0Abdullah Alotaibi1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe idea of [λ, μ]-almost convergence (briefly, F[λ, μ]-convergence) has been recently introduced and studied by Mohiuddine and Alotaibi (2014). In this paper first we define a norm on F[λ, μ] such that it is a Banach space and then we define and characterize those four-dimensional matrices which transform F[λ, μ]-convergence of double sequences x=(xjk) into F[λ, μ]-convergence. We also define a F[λ, μ]-core of x=(xjk) and determine a Tauberian condition for core inclusions and core equivalence.http://dx.doi.org/10.1155/2014/152910 |
| spellingShingle | S. A. Mohiuddine Abdullah Alotaibi Generalized Almost Convergence and Core Theorems of Double Sequences Abstract and Applied Analysis |
| title | Generalized Almost Convergence and Core Theorems of Double Sequences |
| title_full | Generalized Almost Convergence and Core Theorems of Double Sequences |
| title_fullStr | Generalized Almost Convergence and Core Theorems of Double Sequences |
| title_full_unstemmed | Generalized Almost Convergence and Core Theorems of Double Sequences |
| title_short | Generalized Almost Convergence and Core Theorems of Double Sequences |
| title_sort | generalized almost convergence and core theorems of double sequences |
| url | http://dx.doi.org/10.1155/2014/152910 |
| work_keys_str_mv | AT samohiuddine generalizedalmostconvergenceandcoretheoremsofdoublesequences AT abdullahalotaibi generalizedalmostconvergenceandcoretheoremsofdoublesequences |