ON CONVEX-FUNCTIONS HAVING POINTS OF GATEAUX DIFFERENTIABILITY WHICH ARE NOT POINTS OF FRECHET DIFFERENTIABILITY

被引：23

作者：

BORWEIN, JM

FABIAN, M

机构：

[1] UNIV WATERLOO, DEPT COMBINATOR & OPTIMIZAT, WATERLOO N2L 3G1, ONTARIO, CANADA

[2] CZECH TECH UNIV, FAC MACHINE ENGN, CS-12800 PRAGUE 2, CZECHOSLOVAKIA

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 1993年 / 45卷 / 06期

关键词：

GATEAUX DIFFERENTIABILITY; FRECHET DIFFERENTIABILITY; WEAK HADAMARD DIFFERENTIABILITY; (NOT)CONTAINING L1; RENORMING; WEAK-ASTERISK KADEC PROPERTY; CONVEX FUNCTIONS; NONCOMPACT OPERATORS;

D O I：

10.4153/CJM-1993-062-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the relationships between Gateaux, Frechet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we provide related characterizations of infinite dimensional Banach spaces and of Banach spaces containing l1BAR. Explicit examples are given. Some renormings of WCG Asplund spaces are made in this vein.

引用

页码：1121 / 1134

页数：14

共 19 条

[1]

BORWEIN JM, 1992, CORR9204 U WAT TECHN

[2]

BORWEIN JM, IN PRESS CANAD MATH

[3]

BORWEIN JM, ASPLUND SPACES SEQUE

[4]

Deville R., 1993, PITMAN MONOGRAPHS SU, V64