Banach空间中关于(H,η)-增生算子的一类新变分包含组问题

数学季刊 ›› 2008, Vol. 23 ›› Issue (4): 565-573.

Banach空间中关于(H,η)-增生算子的一类新变分包含组问题

1. College of Mathematics and Computer,Hebei University,Baoding 071002,China2. College of Technology,North China Electric Power University,Baoding 071051,China

收稿日期:2006-12-30 出版日期:2008-12-30 发布日期:2023-09-15
作者简介: LIU Ying(1977-), female, native of Xingtai, Hebei, a lecturer of Hebei University, M.S.D., engages in nonlinear function analysis; CHEN Yong-li(1981-), male, native of Cangzhou, Hebei, an assistant of North China Electric Power University, engages in nonlinear function analysis; HE Zhen(1944-), male, native of Tianjin, a professor of Hebei University, M.S.D,, engages in nonlinear function analysis.
基金资助:

A New System of Variational Inclusions with (H,η)-accretive Operators in Banach Spaces

1. College of Mathematics and Computer,Hebei University,Baoding 071002,China2. College of Technology,North China Electric Power University,Baoding 071051,China

Received:2006-12-30 Online:2008-12-30 Published:2023-09-15
About author: LIU Ying(1977-), female, native of Xingtai, Hebei, a lecturer of Hebei University, M.S.D., engages in nonlinear function analysis; CHEN Yong-li(1981-), male, native of Cangzhou, Hebei, an assistant of North China Electric Power University, engages in nonlinear function analysis; HE Zhen(1944-), male, native of Tianjin, a professor of Hebei University, M.S.D,, engages in nonlinear function analysis.

摘要/Abstract

摘要： In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new (H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.

关键词: q-uniformly smooth Banach space;(H,η)-accretive operator, resolvent operator technique, system of variational inclusion, iterative algorithm

Abstract: In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new (H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.

Key words: q-uniformly smooth Banach space;(H,η)-accretive operator, resolvent operator technique, system of variational inclusion, iterative algorithm

中图分类号:

O177.91

刘英, 陈永利, 何震. Banach空间中关于(H,η)-增生算子的一类新变分包含组问题[J]. 数学季刊, 2008, 23(4): 565-573.

LIU Ying, CHEN Yong-li, HE Zhen. A New System of Variational Inclusions with (H,η)-accretive Operators in Banach Spaces[J]. Chinese Quarterly Journal of Mathematics, 2008, 23(4): 565-573.

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