￠—半压缩算子和￠—强增殖算子方程的迭代

设E是任意实Banach空间,K是E的非空闭凸子集,T：K→K是一致连续￠-半压缩映像且值域有界。设{an},{bn},{cn},{a'n},{b'n}和{c'n}是[0,1]中的序列且满足条件：Ⅰ）an bn cn=a'n b'n c'n=1,任意n≥0;Ⅱ）limbn=limb'n=limc'n=0;Ⅲ）∑n=0^∞bn=∞;Ⅳ）cn=o(bn).对任意给定的x0,u0,v0∈K,定义Ishikawa迭代{xn}如下：{xn 1=anxn bnTyn cnun,yn=a'nxn b'nTxn c'nvn(任意n≥0),其中{un}和{vn}是K中两个有界序列。则{xn}强收敛于T的唯一不动点。最后研究了￠-强增殖算子方程解的Ishikawa迭代收敛性。     

Noncompact infinite optimization and equilibria of constrained games in generalized convex spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＩｂｅａｎｙ (ｆｉｎｉｔｅｏｒｉｎｆｉｎｉｔｅ)ｉｎｄｅｘｓｅｔａｎｄｆｏｒｅａｃｈｉ∈Ｉ,Ｘｉｂｅａｔｏｐｏｌｏｇｉｃａｌｓｐａｃｅ.ＷｅｕｓｅｔｈｅｎｏｔａｔｉｏｎＸ =∏ｉ∈ＩＸｉ　ａｎｄ　Ｘｉ=∏ｊ∈Ｉ,ｊ≠ｉＸｊ.Ｆｏｒｅａｃｈｘ∈Ｘ ,ｘｉｄｅｎｏｔｅｓｉｔｓｉｔｈｃｏｏｒｄｉｎａｔｅａｎｄｘｉｔｈｅｐｒｏｊｅｃｔｉｏｎｏｆｘｏｎＸｉ.Ｗｒｉｔｅｘ=(ｘｉ,ｘｉ) .Ｆｏｒｅａｃｈｉ∈Ｉ,ｌｅｔＦｉ:Ｘｉ → 2 Ｘｉｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇａｎｄｆｉ:Ｘ →Ｒ …     

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.     

Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces

A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.     

COINCIDENCE THEOREMS IN PRODUCT G-CONVEX SPACES

By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.     

对没有凸值的连续性的集值映象的最佳逼近定理

本和引入和研究一类具有弱凸图的集值映象，对这类映象证明了某些新的重合定理，最佳逼近和不动点定理。     

广义凸空间内的KKM型定理和极小极大不等式及鞍点定理

本文在非紧G-凸空间内对具有有限闭值和有限开值的G-KKM,广义G-KKM和广义S-KKM映象建立了某些新的KKM型定理。应用这些KKM型定理,在G-凸空间内得到了新的 Ky Fan型极小极大不等式和鞍点定理。这些结论推广了最近文献中的许多已有结果。     

PARETO EQUILIBRIA OF MULTICRITERIA GAMES WITHOUT COMPACTNESS，CONTINUITY AND CONCAVITY

ＰＡＲＥＴＯＥＱＵＩＬＩＢＲＩＡＯＦＭＵＬＴＩＣＲＩＴＥＲＩＡＧＡＭＥＳＷＩＴＨＯＵＴＣＯＭＰＡＣＴＮＥＳＳ,ＣＯＮＴＩＮＵＩＴＹＡＮＤＣＯＮＣＡＶＩＴＹＤｉｎｇＸｉｅｐｉｎｇ（丁协平）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ．ｂｙｕｓｉｎｇａｍｉｎ...     

Generalized Strongly Nonlinear Quasi-Complementarity Problems

ＧＥＮＥＲＡＬＩＺＥＤＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＱＵＡＳＩ－ＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＳＬｉＨｏｎｇ－ｍｅｉ（李红梅）ＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｃｈｅｎｇｄｕ（Ｒｅ...     

多值1—集—压缩不动点的注记

设X是一Banach空间,CK(X)表X的一切非空凸子集的族。P表X内一锥和α表X上的Kuratowski非紧性测度。有关概念、术语和记号,可参见[2,3]。利用[3]内多值凝聚映象的不动点指数理论和类似于[3]的定理3.2证明中的论证方法,