Banach空间中的隐式集值变分包含的一种扰动算法

在Banach空间中研究了一类新的变分包含——隐式集值变分包含问题，得到了隐式变分包含解的等价性与存在性命题及其解的扰动算法，推广、改进了国内外近期获得的一些结果．     

广义非线性变分包含的带误差的近似点算法

引入和研究了一类新的广义非线性变分包含．在Hilbert空间中利用与极大η-单调映象相联系的预解算子的性质，对新的广义非线性变分包含建立了一个新的寻求近似解的带误差的近似点算法，并证明了求近似解序列强收敛于精确解．其所得结果是近期相关结果的改进和推广．     

Banach空间中无限族广义集值拟变分包含

推广了Banach空间中广义拟变分包含的概念，研究了无限族广义集值拟变分包含的解的存在性及其迭代逼近问题．所得结果改进和推广了一些最新的成果．     

一类集值非线性混合变分包含问题的逼近解

在Hilbert空间中讨论了一类集值非线性混合变分包含问题逼近解的存在性,建立了变分包含问题与其预解方程的等价性,获得了3个迭代算法并研究了算法的收敛性．该结果推广统一了近期一些学者关于变分包含问题的相关结果．     

广义非线性含参隐拟变分包含解的灵敏性分析

引入并研究了一类新的广义非线性含参隐拟变分包含,用预解算子方法证明了其解的存在性,并在H ilbert空间中分析了这类变分包含解的灵敏性,这些结果改进和推广了近期文献的相关结果.     

Banach空间中的多值拟变分包含

引入和研究了Banach空间中的多值拟变分包含问题．借助预解算子技巧,建立了某些解的存在性定理及解的迭代逼近．文中所给出的结果改进和推广了许多人的最新结果．     

关于fuzzy映射的完全广义混合强非线性变分包含

引入并研究了Hilbert空间中一类新的关于fuzzy映射的完全广义混合强非线性变分包含，利用极大单调映射的预解算子技巧构造迭代算法．并证明此变分包含的解的存在性及由迭代算法所生成的迭代序列的收敛性。所得结果改进并推广以往所得的相应结果。     

一类含参广义集值拟变分包含组的解的灵敏性分析

本文引入了一类新的含参广义集值拟变分包含组,应用隐预解算子技巧,建立了该类变分包含组与一类不动点问题的等价性,在适当的条件下,分析了含参广义集值拟变分包含组的解的灵敏性,所得结果推广改进了最新文献中的许多结果．     

Banach空间中k-次增生型变分包含解的存在与收敛性

在实自反Banach空间中,引入并研究一类k-次增生型变分包含问题,证明了这类变分包含解的存在与唯一性,并在去掉α_n→0,β_n→0(n→∝)以及序列{x_n)和{_η(g(x_n))}有界限制的条件下,建立了k-次增生型变分包含和变分不等式解的具有混合误差的多步迭代序列的强收敛性定理,给出了收敛率的估计式,从而改进和推广了前人的研究结果.     

广义多值拟变分包含的灵敏性分析

借助隐预解算子技巧来研究广义多值拟变分包含的灵敏性分析．所得结果改进、推广和统一了文献中的一些结果．     

The <Emphasis Type="Italic">p</Emphasis>-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with (<Emphasis Type="Italic">H</Emphasis>,η)-monotone operators

In this paper, we introduce and study a new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators which contains variational inequalities, variational inclusions, systems of variational inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (H,η)-monotone operators, we prove the existence of solutions and the convergence of some new p-step iterative algorithms for this system of generalized mixed quasi-variational inclusions and its special cases. The results in this paper unifies, extends and improves some known results in the literature.     

对带误差项的Banach空间中完全广义集值拟变分包含的摄动迭代算法

研究了一类新的实Banach空间中的广义集值拟变分包含:f∈N(x，y) M(z，v) W(g(u)-h(w)，u)，它包含了近几年许多作者所作的变分包含同题．在买Banach空间中，利用极大增生算子的性质，建立了Banach空间中的广义集值拟变分包含和不动点问题间的等价性．利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解．本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果。     

The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (<Emphasis Type="Italic">A</Emphasis>, <Emphasis Type="Italic">η</Emphasis>, <Emphasis Type="Italic">m</Emphasis>)-accretive operators

In this paper, we introduce and study a new system of variational inclusions with (A, η, m)-accretive operators which contains variational inequalities, variational inclusions, systems of variational inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, η, m)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multi-step iterative algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.      

Existence and iterative approximation of solutions of a system of general variational inclusions

In this paper, we consider a system of general variational inclusions in q-uniformly smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for the system of general variational inclusions. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature.     

对带误差项的广义集值变分包含的近似点算法

研究一类新的广义集值变分包含：０∈Ｎ（ｗ,ｙ）＋Ａ（ｚ,ｕ）,它包合了近几年许多作者所作的变分包合问题．在实Ｈｉｌｂｅｒｔ空间中,利用极大单调算子的性质,建立了广义集值变分包合和不动点问题间的等价性．利用这种等价性,建立了一些摄动迭代算法,并证明了近似解序列强收敛于精确解．本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果．     

Existence and iterative approximation of solutions of some systems of variational inequalities and inclusions

In 1968, Brézis [Ann. Inst. Fourier (Grenoble), 18 (1) (1968) 115-175] initiated the study of the existence theory of a class of variational inequalities later known as variational inclusions, using proximal-point mappings due to Moreau [Bull. Soc. Math. France, 93 (1965) 273-299]. Variational inclusions include variational, quasi-variational, variational-like inequalities as special cases. In 1985, Pang [Math. Prog. 31 (1985) 206-219] showed that a variety of equilibrium models can be uniformly modelled as a variational inequality defined on the product sets equivalent to a system of variational inequalities and discuss the convergence of method of decomposition for system of variational inequalities. Motivated by the recent research work in this directions, we consider some systems of variational (-like) inequalities and inclusions; develop the iterative algorithms for finding the approximate solutions and discuss their convergence criteria. Further, we study the sensitivity analysis of solution of the system of variational inclusions. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-step iterative methods for general variational inclusions in L P spaces

In this paper, we show that the general variational inclusions are equivalent to the fixed point problem. We use this equivalence to discuss the existence of the variational inclusions in L ^p spaces. Using the technique of the updating solution, we suggest some three-step iterative methods for solving the general variational inclusion. We also consider the convergence analysis of the proposed iterative methods under some mild conditions. Since the general variational inclusions include several classes of variational inequalities and optimization problems as special cases, results proved in this paper continue to hold for these problems.     

On random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings

In this paper, we introduce and study the random variational inclusions with random fuzzy and random relaxed cocoercive mappings. We define an iterative algorithm for finding the approximate solutions of this class of variational inclusions and establish the convergence of iterative sequences generated by proposed algorithm. Our results improve and generalize many known corresponding results.     

Generalized multivalued nonlinear quasivariational inclusions

In this paper, we introduce and study a few classes of generalized multivalued nonlinear quasivariational inclusions and generalized nonlinear quasivariational inequalities, which include many classes of variational inequalities, quasivariational inequalities and variational inclusions as special cases. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for finding the approximate solutions of these classes of quasivariational inclusions and quasivariational inequalities. We establish the existence of solutions for this generalized nonlinear quasivariational inclusions involving both relaxed Lipschitz and strongly monotone and generalized pseudocontractive mappings and obtain the convergence of iterative sequences generated by the algorithms. Under certain conditions, we derive the existence of a unique solution for the generalized nonlinear quasivariational inequalities and obtain the convergence and stability results of the Noor type perturbed iterative algorithm. The results proved in this paper represent significant refinements and improvements of the previously known results in this area.