Título inglés | Weak moduli of convexity. |
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Título español | Módulos débiles de convexidad. |
Autor/es | Alonso, Javier ; Ullán, Antonio |
Organización | Dep. Mat. Univ. Extremadura, Badajoz, España |
Revista | 0213-8743 |
Publicación | 1991, 6 (1): 47-49, 4 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | Let E be a real normed linear space with unit ball B and unit sphere S. The classical modulus of convexity of J. A. Clarkson [2] δE(ε) = inf {1 - 1/2||x + y||: x,y Î B, ||x - y|| ≥ ε} (0 ≤ ε ≤ 2) is well known and it is at the origin of a great number of moduli defined by several authors. Among them, D. F. Cudia [3] defined the directional, weak and directional weak modulus of convexity of E, respectively, as δE(ε,g) = inf {1 - 1/2||x + y||: x,y Î B, g(x-y) ≥ ε} δE(ε,f) = inf {1 - 1/2 f(x,y): x,y Î B, ||x - y|| ≥ ε} δE(ε,f,g) = inf {1 - 1/2 f(x,y): x,y Î B, g(x-y) ≥ ε} where 0 ≤ ε ≤ 2 and f,g Î S' (unit sphere of the topological dual space E'). D. F. Cudia [3] has shown the close connection existing between these moduli and various differentiability conditions of the norm in E'. In this note we study these moduli from a different point of view, then we analyze some of its properties and we see that it is possible to characterize inner product spaces by means of them. |
Clasificación UNESCO | 120203 |
Palabras clave español | Espacios normados ; Espacios con producto interno ; Convexidad ; Módulo de convexidad |
Acceso al artículo completo |