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．     

Banach空间中完全广义混合隐似平衡问题的辅助原理和迭代算法

在Banach空间中利用双线性连续泛函F代替内积引进了新的一类完全广义混合隐似平衡问题，引进了F强单调的概念，提出了该平衡问题的广义辅助问题，证明了广义辅助问题的收敛定理，给出了新的算法和由此算法产生的迭代序列的收敛特征．     

求解广义混合隐拟平衡问题的预测修正算法

引入和研究了一类新的具有四元函数的广义混合隐拟平衡问题．这类平衡问题包含了很多已知的广义平衡问题和广义混合隐拟变分不等式问题作为很特殊的情形．利用辅助原理技巧建议和分析了求解广义混合隐拟平衡问题的预测修正迭代算法．所建议算法的收敛性仅需要映象的连续性和部分松弛强单调性．     

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.     

Banach空间的上带松弛共强制的广义隐式变分包含组

本文在Banach空间上引入和研究了一类带松弛共强制的广义隐式变分包含组（SNSIVI）．使用M增值算子的预解算子技术，我们构造了一类新的迭代算法逼近这类隐式变分包含组，且在q-一致平滑Banach空间上证明了这类迭代算法的收敛性．我们的结果推广和改进了最近的相关工作．     

多值一般混合隐似平衡问题解的迭代算法

引入和研究了多值一般混合隐似平衡问题．运用辅助原则的技巧提出和分析了求解多值一般混合隐似平衡问题的预测校正迭代算法,并在较弱的条件下证明了算法的收敛性．     

广义似平衡问题与有限簇非扩张映象的强收敛定理

在Hilbert空间的框架下,为寻求广义似平衡问题(GELP)的解集与非扩张映象的不动点集的公共元,引入和研究了一种新的混合迭代算法.在一定的条件下,用黏性逼近法证明了迭代序列逼近于这一公共元的某些强收敛定理.所得结果改进和推广了文献的相应结果.     

一类广义非线性混合拟变分包含组

本文引入了一类新的带松弛单调映射和松弛Lipschitz映射的广义非线性混合拟变分包含组 ,构造了求解该类变分包含组的迭代算法 ,证明了该类变分包含组解的存在性以及由本文构造的迭代算法产生的迭代序列的强收敛性 .所得结果推广和改进了大量文献中的最新结果[1 5 ] .     

Banach空间中一类广义混合非线性隐拟变分包含解的三步迭代

本文引入并研究了实Banach空间中一类新的广义混合非线性隐拟变分包含 ,通过对实Banach空间中的m 增生映象运用Nadler定理和Michael选择定理 ,构建了这类新的广义变分包含解的三步迭代算法 ,并证明了其解的存在性和由迭代算法生成的迭代序列的收敛性     

g-Eta-单调映像和解广义隐似变分包含的预解算子技巧

引入一类新的g-Eta-单调映像和一类涉及g-Eta-单调映像的广义隐似变分包含；定义了g-Eta-单调映像的预解算子，并证明了其Lipschitz连续性；分析和给出了这类涉及g-Eta-单调映像的广义隐似变分包含的迭代算法，并证明了其收敛性．     

Iterative algorithm of solutions for a system of generalized mixed implicity equilibrium problems in reflexive Banach spaces

In this paper, a new system of generalized mixed implicity equilibrium problems involving non-monotone set-valued mappings is introduced and studied in real reflexive Banach spaces. Following the idea of Moudafi, we consider a system of generalized equations problems and show its equivalence with the system of generalized mixed implicity equilibrium problems. By using a fixed point formulation of the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new and unify and generalize some recent results in this field.     

Sensitivity analysis for a system of generalized mixed implicit equilibrium problems in uniformly smooth Banach spaces

In this paper, a new system of parametric generalized mixed implicit equilibrium problems involving non-monotone set-valued mappings in real Banach spaces is introduced and studied. We first generalize the notion of the Yosida approximation in Hilbert spaces introduced by Moudafi to reflexive Banach spaces. Further, by using the notion of the Yosida approximation, we consider a system of parametric generalized Wiener-Hopf equation problems and show its equivalence to the system of parametric generalized mixed implicit equilibrium problems. By using a fixed point formulation of the system of parametric generalized Wiener-Hopf equation problems, we study the behavior and sensitivity analysis of a solution set of the system of parametric generalized mixed implicit equilibrium problems. We prove that, under suitable assumptions, the solution set of the system of parametric generalized mixed implicit equilibrium problems is nonempty, closed and Lipschitz continuous with respect to the parameters. Our results are new, and improve and generalize some known results in this field.     

Equivalence of generalized mixed complementarity and generalized mixed least element problems in ordered spaces

In this article, we derive some equivalences of generalized mixed non-linear programs, generalized mixed least-element problems, generalized mixed complementarity problems and generalized mixed variational inequality problems under certain regularity and growth conditions. We also generalize the notion of a Z-type map for point-to-set maps. Our results improve and extend recent results in the literature.     

Auxiliary principle and iterative algorithm for a new system of generalized mixed equilibrium problems in Banach spaces

In this paper, we study a new system of generalized mixed equilibrium problems involving skew-symmetric bifunctions (SGMEP) in reflexive Banach spaces. A system of auxiliary mixed equilibrium problems (SAMEP) for solving the SGMEP is introduced and the existence and uniqueness of the solutions of the SAMEP is first proved. Next, by using the auxiliary principle technique, a new iterative algorithm to compute the approximate solutions of the SGMEP is suggested and analyzed. Finally, the strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild conditions. These results improve, unify and generalize some known results in recent literature.     

A new class of bilevel generalized mixed equilibrium problems in Banach spaces

A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.     

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint corre- spondences are proved in FC-spaces.By using these equilibrium existence theorems,some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces.These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.     

G -凸空间中的广义对策和广义矢量拟平衡问题组

该文在广义G -凸空间中引入并研究了一类新的广义矢量拟平衡问题组(SGVQEP).利用作者的一族集值映象的极大元存在定理,证明了广义对策的一个新的平衡存在定理.作为应用,在非紧乘积G -凸空间中证明了SGVQEP解的一些新的存在定理.     

局部FC-一致空间内具有联立广义矢量拟平衡组约束的数学规划(英文)

在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理.     

System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.