Implicit function theorem without a priori assumptions about normality

被引：13

作者：

Arutyunov A.V. ^{[1
]}

机构：

[1] Peoples Friendship University, Moscow, 117198

来源：

Computational Mathematics and Mathematical Physics | 2006年 / 46卷 / 2期

基金：

俄罗斯基础研究基金会;

关键词：

2-regularity condition; Convex cone; Implicit function theory; Robinson condition;

D O I：

10.1134/S0965542506020023

中图分类号：

学科分类号：

摘要：

The equation F(x, σ) = 0,x K, in which σ is a parameter and x is an unknown taking values in a given convex cone in a Banach space X, is considered. This equation is examined in a neighborhood of a given solution (x*, σ*) for which the Robinson regularity condition may be violated. Under the assumption that the 2-regularity condition (defined in the paper), which is much weaker than the Robinson regularity condition, is satisfied, an implicit function theorem is obtained for this equation. This result is a generalization of the known implicit function theorems even for the case when the cone K coincides with the entire space X. © MAIK "Nauka/Interperiodica" (Russia), 2006.

引用

页码：195 / 205

页数：10

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