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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Hindawi Limited
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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doaj-c63bf26b78ae486080cba3d524e101252020-11-25T00:24:13ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Tomonari Suzuki |
| spellingShingle |
Tomonari Suzuki p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 Abstract and Applied Analysis |
| author_facet |
Tomonari Suzuki |
| author_sort |
Tomonari Suzuki |
| title |
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_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_sort |
p-uniform convexity and q-uniform smoothness of absolute normalized norms on ℂ2 |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2014/746309 |
| work_keys_str_mv |
AT tomonarisuzuki puniformconvexityandquniformsmoothnessofabsolutenormalizednormsonc2 |
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1725353202128257024 |