Banach空间中求解变分包含的(H,m)-算子和预解算子技巧

Banach空间中求解变分包含的(H,m)-算子和预解算子技巧

摘要

在Banach中引进了1类新的广义增生算子即(H;m)-增生算子. 通过研究(H;m)-增生算子的性质，我们把联系基本的m-增生算子的预解算子概念扩张到新的(H;m)-增生算子. 鉴于预解算子技巧，我们给出了Banach空间中1类与(H;m)-算子有关的变分包含的逼近解。

关键词：(H，m)-增生算子；预解算子技巧；变分包含；迭代算法.

H-Accretive Operators and Resolvent Operators Technique for Solving Variational Inclusions in Banach Spaces

Abstract

In this paper, we first introduce a new class of generalized accretive operators，i.e., (H;m)-accretive operators in Banach spaces. By investigating the properties of (H;m)-accretive operators, we extend the concept of resolvent operators associated with the classical m-accretive operators to the new (H;m)-accretive operators. In terms of the resolvent operator technique, we give the approximate solution for a class of variational inclusions involving (H;m)-accretive operators in Banach spaces.

Keywords：(H;m)-accretive operators；Resolvent operator technique；Variational inclusions；Iterative algorithm。