自反Banach空间内混合非线性似变分不等式解的算法*

本文在自反Banach空间内研究了一类混合非线性似变分不等式应用作者得到的一个极小极大不等式,对这类混合非线性似变分不等式的解,证明了几个存在唯一性定理其次由应用辅助问题技巧,作者建议了一个计算此类混合非线性似变分不等式的近似解的创新算法最后讨论收敛性准则.     

广义集值强非线性混合似变分不等式解的迭代逼近

延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式．证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性．利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法,最终证明了这类广义强非线性混合似变分不等式解的存在性及由算法生成的迭代序列的收敛性．     

广义集值强非线性混合似变分不等式的辅助原理和三步迭代算法

使用辅助原理技巧研究了一类广义集值强非线性混合变分不等式．证明了此类集值强非线性混合变分不等式辅助问题解的存在性和唯一性;构建了一个新的三步迭代算法,通过辅助原理技巧,构建并计算此类非线性混合变分不等式的近似解,进一步证明非线性混合变分不等式解的存在性以及由算法产生的三个序列的收敛性．所得结论推广了近年来许多混合变分不等式和准变分不等式以及他们的有关结果．     

Banach空间中强伪单调变分不等式解的唯一性和稳定性

在自反Banach空间中证明强伪单调变分不等式解的存在唯一性定理.在此基础上研究扰动变分不等式解的稳定性.此外,也在有限维空间中得到了强拟单调变分不等式解的存在性定理.     

摩擦问题中的边界混合变分不等式

本文以弹性力学中的摩擦问题为背景,讨论了非线性、不可微的混合变分不等式解的存在唯一性,给出相应的边界变分不等式及其解的存在唯一性。为使用边界元方法数值求解提供了理论依据。     

自反Banach空间中广义混合双线性变分不等式解的存在性

介绍了自反B anach空间中一类广义混合双线性型变分不等式,利用极大极小不等式和辅助变分原理技术证明了这类混合双线性型变分不等式解的存在性与唯一性.     

广义集值强非线性混合似变分不等式解的迭代逼近

辅助原理的技巧被延拓来研究一类取非紧值的集值映象的广义强非线性混合似变分不等式.首先,证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性.其次,利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法.最后,不仅证明了这类广义强非线性混合似变分不等式解的存在性,而且证明了由算法生成的迭代序列的收敛性.     

关于混合拟似变分包含问题的解的迭代算法

本文对混合拟似变分包含问题提出新的辅助变分不等式,首先证明辅助变分不等式存在唯一解.然后,通过这一辅助形式建立混和拟似变分包含问题解的迭代算法.最后讨论在新的算法下迭代解的收敛性.     

半准内凸函数及其广义变分不等式

研究拓扑向量空间半准内凸函数的特性,给出半内凸弧方向可微函数的最小值可由一类似变分不等式问题的解表示及一类广义变分不等式解的唯一性。     

辅助原理技术在广义混合似变分不等式中的应用

通过使用辅助原理技术证明了Hilbert空间中-类广义混合似变分不等式解的存在性,并给出一种算法计算此类变分不等式的近似解.     

Existence and iterative algorithm of solutions for a system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems in Banach spaces

In this paper, we introduce and study a new system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems. Firstly, we prove the existence and uniqueness of solutions of the auxiliary problems for the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems. Secondly, an iterative algorithm for solving the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems is constructed by using this existence and uniqueness result. Finally, we show the existence of solutions of the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems and discuss the convergence analysis of this algorithm. These results improve, unify and generalize many corresponding known results given in literatures.     

反Banach空间内涉及广义混合似臣分不等式问题的双水平广义混合平衡问题

在自反Banach空间内,引入和研究了一类新的涉及广义混合似变分不等式问题的双水平广义混合平衡问题(BGMEP).首先,为了计算BGMEP的近似解,引入了一类辅助广义混合平衡问题(AGMEP).由使用一极小极大不等式,在没有任何强制条件的相当温和假设下,证明了AGMEP解的存在性和唯一性.利用辅助原理技巧,建议和分析了一类计算BGMEP的近似解的新迭代算法.在没有任何强制条件的相当温和假设下,证明了由算法生成的迭代序列的强收敛性.这些结果是新的并且推广了这一领域内某些最近结果.     

The auxiliary principle and an algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces

In this paper, we introduce and study a new system of generalized set-valued mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set-valued mixed variational-like inequality problems. At first, the existence and uniqueness of solutions of the auxiliary problems for (SGSMVLIP) is shown. Next, an iterative algorithm for solving (SGSMVLIP) is constructed by using the existence and uniqueness result. Finally, we prove the existence of solutions of (SGSMVLIP) and discuss the convergence analysis of the algorithm. These results improve, unify and generalize many corresponding known results given in the literature.     

Existence of Solutions and an Algorithm for Mixed Variational-Like Inequalities in Banach Spaces

In this paper, we study the class of mixed variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to the author, some existence and uniqueness theorems for solutions of mixed variational-like inequalities are proved. Next, by applying the auxiliary problem technique, we suggest an innovative iterative algorithm to compute approximate solutions of the mixed variational-like inequality. Finally, convergence criteria are also discussed. This research was supported by NSF, Sichman Education Department of China, Projects 2003A081 and SZD0406. The author expresses his sincere thanks to Professor H.P. Benson and the anonymous referees for careful comments leading to the present version of this paper.     

自反Banach空间内一类新的广义混合平衡问题组的辅助原理和逼近可解性

在自反Banach空间内引入和研究了一类新的涉及广义混合似变分不等式问题的广义混合平衡问题组(SGMEP)．首先,为了求解 SGMEP,引入了一类辅助广义混合平衡问题组(SAGMEP)．在没有任何强制条件的相当温和假设下, 对SAGMEP证明了解的存在性和唯一性．其次, 利用辅助原理技巧,对求解SGMEP建议和分析了一类新的迭代算法．最后,在没有任何强制条件的相当温和假设下,证明了由算法生成的迭代序列的强收敛性．这些结果改进、统一和推广了这一领域内某些最近结果．