Proximal analysis in reflexive smooth Banach spaces

被引：14

作者：

Bounkhel, M. ^{[1
]}

Al-Yusof, R. ^{[1
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 07期

关键词：

Proximal subdifferential; Proximal normal cone; Reflexive Banach space; Sweeping process; Density theorem; REGULARITY;

D O I：

10.1016/j.na.2010.04.077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we introduce and study a new proximal normal cone in reflexive Banach spaces in terms of a generalized projection operator. Two new variants of generalized proximal subdifferentials are also introduced in reflexive smooth Banach spaces. The density theorem for both proximal subdifferentials has been proved in p-uniformly convex and q-uniformly smooth Banach spaces. Various important properties and applications of our concepts are also proved. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1921 / 1939

页数：19

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