一类ψ-强增生型变分包含问题解的存在性与迭代逼近

本研究Banach空间中一类新的ψ-强增生型变分包含问题．在实的自反的光滑Banach空间中．证明了这类变分包含问题解的存在唯一性及其带误差的Ishikawa迭代程序的收敛性．本结果是张石生教授等人的早期与最近的结果的改进与推广．     

一类新的Ф-强增生型变分包含问题

本文研究了Banach空间中一类新的Ф-强增生型变分包含问题．在实自反Banach空间中，证明了这类变分包含问题解的存在唯一性及其带有混合误差项的Ishikawa迭代程序的收敛性．本文结果是张石生教授和曾六川教授等人的早期与最近的结果的改进与推广．     

Banach空间中m-增生型变分包含解的具误差的迭代逼近

本文在Banach空间中研究一类新的增生型变分包含解的存在性及其具误差的Ishikawa迭代序列的收敛性,本文结果改进与推广了近期文献中的相应结果。     

Banach空间中强增生型变分包含解的具误差的Ishikawa迭代逼近

该文研究Ｂａｎａｃｈ空间中一类强增生型变分包含解的存在性及其具误差的Ｉｓｈｉｋａｗａ迭代程序的收敛性问题．该文结果是几位作者早期与最近的相应结果的改进和推广．     

ψ-强增生型变分包含问题解的Ishikawa迭代逼近

在实自反Banach空间中,引入和研究了一类新的ψ强增生型变分包含问题,证明了这类变分包含问题解的存在唯一性及其带有误差项的Ishikawa迭代程序的收敛性.本文结果改进、发展和统一了张石生教授和曾六川教授等人的一系列相关结果.     

Banach空间中ψ—强增生型变分包含问题解的Ishikawa迭代逼近

本文引入和研究Ｂａｎａｃｈ空间中ψ－强增生型变分包含解的存在性、唯一性及Ｉｓｈｉｋａｗａ迭代过程收敛问题,所得结果改进和推广了「２,３,５－９,１２－１４」等相关结果。     

Banach空间中φ-强增生型变分包含问题解的Ishikawa迭代逼近

本文引入和研究Banach空间中φ-强增生型变分包含解的存在性、唯一性及Ishikawa迭代过程收敛问题,所得结果改进和推广了[2,3,5-9,12-14]等相关结果.     

一类新的k-次增生型变分包含解的存在性及其具有混合误差项的Ishikawa迭代逼近

在实自反Banach空间中,引入和研究了一类新的k-次增生型变分包含问题,证明了这类变分包含解的存在性、唯一性及其具有混合误差项的Ishikawa迭代程序的收敛性.本文结果本质地改进、发展和统一了张石生和曾六川等人的一系列相关结果.     

一类φ-强增生型变分包含问题解的存在性与迭代逼近

本文研究Banach空间中一类新的φ-强增生型变分包含问题。在实的自反的光滑Ba-nach空间中,证明了这类变分包含问题解的存在唯一性及其带误差的Ishikawa迭代程序的收敛性。本文结果是张石生教授等人的早期与最近的结果的改进与推广。     

一类新的φ-强增生型变分包含问题解的存在性与迭代逼近

本文研究了Banach空间中一类新的φ-强增生型变分包含问题,在实自反Banach空间中,证明了这类变分包含问题解的存在唯一性及其带有混合误差项的Ishikawa迭代程序的收敛性,本文结果是张石生教授和曾六川教授等人的早期与最近的结果的改进与推广.     

On a new system of nonlinear A-monotone multivalued variational inclusions

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated with A-monotone mappings in Hilbert spaces. We also prove the existence of solutions for the nonlinear multivalued variational inclusions and the convergence of iterative sequences generated by the 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.     

Iterative Schemes for Multivalued Quasi Variational Inclusions

In this paper, we suggest and analyze a class of iterative schemes for solving multivalued quasi variational inclusions using the resolvent operator method. As special cases, we obtain a number of known and new iterative schems for solving variational inequalities and related optimization problems. The results obtained in this represent an improvement and a significant refinement of previously known results.     

集值非线性混合变分包含问题解的存在性及其算法

本文研究一类广义集值非线性混合变分包含问题,讨论了解的存在性,给出了逼 近解的双步迭代算法,推广统一了一些近期结果.     

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。     

A class of history-dependent systems of evolution inclusions with applications

This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex subdifferential form. Using a surjectivity result for multivalued maps and a fixed point argument for a history-dependent operator, we prove that the system has a unique solution. We conclude with two examples of an evolutionary differential variational–hemivariational inequality and of a dynamic frictional contact problem in mechanics, which illustrate the abstract results.     

Banach空间中的广义非线性混合型拟变分包含

在Banach空间中讨论一类新的广义非线性混合型拟变分包含问题.用预解算子的概念,建立了一种解此类问题的算法.所得结果改进、推广和统一了文献中的一些结果.     

Weighted Variational Inequalities

In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities. It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems of generalized vector variational inequalities. The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees for comments and suggestions improving the final draft of this paper.     

带状态约束的抛物型变分不等式的最优控制

利用非光滑分析和半变分不等式的一些方法和结果，研究了一类带状态约束的具有非线性、不连续以及非单调多值项的抛物型变分不等式的优化控制问题以及它的逼近等，推广了一些已有的结果．     

Generalized solutions of quasi variational inequalities

This paper deals with multivalued quasi variational inequalities with pseudo-monotone and monotone maps. The primary objective of this work is to show that the notion of generalized solutions can be employed to investigate multivalued pseudo-monotone quasi variational inequalities. It is a well-known fact that a quasi variational inequality can conveniently be posed as a fixed point problem through the so-called variational selection. For pseudo-monotone maps, the associated variational selection is a nonconvex map, and the fixed point theorems can only be applied under restrictive assumptions on the data of quasi variational inequalities. On the other hand, the generalized solutions are defined by posing a minimization problem which can be solved by a variant of classical Weierstrass theorem. It turns out that far less restrictive assumptions on the data are needed in this case. To emphasis on the strong difference between a classical solution and a generalized solution, we also give a new existence theorem for quasi variational inequalities with monotone maps. The main existence result is proved under a milder coercivity condition. We also relax a few other conditions from the monotone map. Due to its flexibility, it seems that the notion of generalized solutions can be employed to study quasi variational inequalities for other classes of maps as well.