Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions
<p/> <p>We introduce the vector-valued sequence spaces <inline-formula> <graphic file="1029-242X-2010-457892-i1.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-457892-i2.gif"/></inline-formula>, and <inlin...
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2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/457892 |
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doaj-76b4b8e0654e4bc4be69a33d2f74a83b2020-11-25T02:28:17ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-0120101457892Generalized Vector-Valued Sequence Spaces Defined by Modulus FunctionsIşik Mahmut<p/> <p>We introduce the vector-valued sequence spaces <inline-formula> <graphic file="1029-242X-2010-457892-i1.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-457892-i2.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2010-457892-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-457892-i4.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2010-457892-i5.gif"/></inline-formula>, using a sequence of modulus functions and the multiplier sequence <inline-formula> <graphic file="1029-242X-2010-457892-i6.gif"/></inline-formula> of nonzero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly <inline-formula> <graphic file="1029-242X-2010-457892-i7.gif"/></inline-formula>-Cesàro summable with respect to the modulus function <inline-formula> <graphic file="1029-242X-2010-457892-i8.gif"/></inline-formula> then it is <inline-formula> <graphic file="1029-242X-2010-457892-i9.gif"/></inline-formula>-statistically convergent.</p>http://www.journalofinequalitiesandapplications.com/content/2010/457892 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Işik Mahmut |
| spellingShingle |
Işik Mahmut Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions Journal of Inequalities and Applications |
| author_facet |
Işik Mahmut |
| author_sort |
Işik Mahmut |
| title |
Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions |
| title_short |
Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions |
| title_full |
Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions |
| title_fullStr |
Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions |
| title_full_unstemmed |
Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions |
| title_sort |
generalized vector-valued sequence spaces defined by modulus functions |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2010-01-01 |
| description |
<p/> <p>We introduce the vector-valued sequence spaces <inline-formula> <graphic file="1029-242X-2010-457892-i1.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-457892-i2.gif"/></inline-formula>, and <inline-formula> <graphic file="1029-242X-2010-457892-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-457892-i4.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2010-457892-i5.gif"/></inline-formula>, using a sequence of modulus functions and the multiplier sequence <inline-formula> <graphic file="1029-242X-2010-457892-i6.gif"/></inline-formula> of nonzero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly <inline-formula> <graphic file="1029-242X-2010-457892-i7.gif"/></inline-formula>-Cesàro summable with respect to the modulus function <inline-formula> <graphic file="1029-242X-2010-457892-i8.gif"/></inline-formula> then it is <inline-formula> <graphic file="1029-242X-2010-457892-i9.gif"/></inline-formula>-statistically convergent.</p> |
| url |
http://www.journalofinequalitiesandapplications.com/content/2010/457892 |
| work_keys_str_mv |
AT i351ikmahmut generalizedvectorvaluedsequencespacesdefinedbymodulusfunctions |
| _version_ |
1724839178518134784 |