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INICIO | 14 de abril de 2024
  

Weak moduli of convexity.

Título inglés Weak moduli of convexity.
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
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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