p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2
We first prove characterizations of p-uniform convexity and q-uniform smoothness. We next give a formulation on absolute normalized norms on ℂ2. Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is not p-uniformly convex.
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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/10.1155/2014/746309 |
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| _version_ | 1832554732892192768 |
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| author | Tomonari Suzuki |
| author_facet | Tomonari Suzuki |
| author_sort | Tomonari Suzuki |
| collection | DOAJ |
| description | We first prove characterizations of p-uniform convexity and q-uniform
smoothness. We next give a formulation on absolute normalized norms on ℂ2. Using
these, we present some examples of Banach spaces. One of them is a uniformly convex
Banach space which is not p-uniformly convex. |
| format | Article |
| id | doaj-art-c63bf26b78ae486080cba3d524e10125 |
| 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-c63bf26b78ae486080cba3d524e101252025-02-03T05:50:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/746309746309p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2Tomonari Suzuki0Department of Basic Sciences, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, JapanWe first prove characterizations of p-uniform convexity and q-uniform smoothness. We next give a formulation on absolute normalized norms on ℂ2. Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is not p-uniformly convex.http://dx.doi.org/10.1155/2014/746309 |
| spellingShingle | Tomonari Suzuki p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 Abstract and Applied Analysis |
| title | p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 |
| title_full | p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 |
| title_fullStr | p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 |
| title_full_unstemmed | p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 |
| title_short | p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 |
| title_sort | p uniform convexity and q uniform smoothness of absolute normalized norms on c2 |
| url | http://dx.doi.org/10.1155/2014/746309 |
| work_keys_str_mv | AT tomonarisuzuki puniformconvexityandquniformsmoothnessofabsolutenormalizednormsonc2 |