uniformly convex space

A normed space is uniformly convex iff $\\forall\\epsilon>0$ there exists $\\delta>0$ that satisfiesfor $\\|x\\|\\leq 1$ $\\|y\\|\\leq 1$ and $\\|x-y\\|>\\epsilon$ $\\Rightarrow$ $\\|\\frac{x+y}{2}\\|\\leq 1$ - $\\delta$ .

For example it is easily seen that the normed space $(\\mathbb{R}^{2},\\|.\\|_{2})$ is uniformly convex space.Also $L^{p}$ and $l^{p}$ spaces for $1<p<\\infty$ are uniformly convex, see J.A. Clarkson, ”Uniformly convex spaces”, Trans. Amer. Math. Society, 40 (1936), 396-414.

单词	UniformlyConvexSpace
释义	uniformly convex space A normed space is uniformly convex iff $\\forall\\epsilon>0$ there exists $\\delta>0$ that satisfiesfor $\\\|x\\\|\\leq 1$ $\\\|y\\\|\\leq 1$ and $\\\|x-y\\\|>\\epsilon$ $\\Rightarrow$ $\\\|\\frac{x+y}{2}\\\|\\leq 1$ - $\\delta$ . For example it is easily seen that the normed space $(\\mathbb{R}^{2},\\\|.\\\|_{2})$ is uniformly convex space.Also $L^{p}$ and $l^{p}$ spaces for $1<p<\\infty$ are uniformly convex, see J.A. Clarkson, ”Uniformly convex spaces”, Trans. Amer. Math. Society, 40 (1936), 396-414.
随便看	Catacaustic catacaustic CatalanNumbers Catalan numbers CatalansConjecture CatalansIdentity Catalan’s conjecture Catalan’s identity CategoricalAlgebra categorical algebra CategoricalDynamics categorical dynamics CategoricalQuantumLMLogicAlgebras categorical quantum LM- logic algebras Categories and precategories CategoriesInPhysics categories in physics CategoriesOfPolishGroupsAndPolishSpaces categories of Polish groups and Polish spaces CategoryOfBorelSpaces category of Borel spaces CategoryOfGroupoids category of groupoids CategoryOfHalgebras category of H * -algebras