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1.
丁协平 《应用数学和力学(英文版)》2005,26(5):563-570
IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ . Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) , z∈A( ^x) . ( 1 ) Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) , z∈A( ^x) . ( 2 ) … 相似文献
2.
By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature. 相似文献
3.
丁协平 《应用数学和力学(英文版)》2014,35(7):925-934
A new bilevel generalized mixed equilibrium problem (BGMEF) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field. 相似文献
4.
张石生 《应用数学和力学(英文版)》2009,30(9):1105-1112
This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently. 相似文献
5.
丁协平 《应用数学和力学(英文版)》2011,32(11):1457-1474
A new bilevel generalized mixed equilibrium problem(BGMEP) involving generalized mixed variational-like inequality problems(GMVLIPs) is introduced and studied in the reflexive Banach spaces.First,an auxiliary generalized mixed equilibrium problem(AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs.By using a minimax inequality,the existence and the uniqueness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions.By using an au... 相似文献
6.
PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS 总被引:4,自引:0,他引:4
A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings 相似文献
7.
We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz. 相似文献
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9.
丁协平 《应用数学和力学(英文版)》2011,32(2):231-240
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. 相似文献
10.
DING Xie-Ping 《应用数学和力学(英文版)》2011,2(32):231-240
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. 相似文献
11.
A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized
mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively
weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by
many other authors. 相似文献
12.
A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors. 相似文献
13.
曾六川 《应用数学和力学(英文版)》2003,24(11):1324-1333
A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the e 相似文献
14.
郭友中 《应用数学和力学(英文版)》1989,10(1):1-24
In this paper the problem of inequality in solid mechanics, the contents of which consist of some main concepts, methods and results of the stationary and evolutionary as well as determinate and random problems in variational principle and variational inequality, is studied in detail. 相似文献
15.
高扬 《应用数学和力学(英文版)》1996,17(10):953-968
CONTACTPROBLEMSANDDUALVARIATIONALINEQUALITYOF2-DELASTOPLASTICBEAMTHEORYDavidYangGao(高扬)(DepartmentofMathematics.VirginiaPolyt... 相似文献
16.
This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.(Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715(2009)),Plubtieng and Punpaeng(Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469(2007)),Colao et al.(Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352(2008)),Yao et al.(Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363(2007)DOI 10.1155/2007/64363),and others. 相似文献
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A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used
to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed
points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational
inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets. 相似文献
19.
Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces 总被引:1,自引:0,他引:1
丁协平 《应用数学和力学(英文版)》2004,25(6):618-626
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature. 相似文献
20.
DING Xie-ping College of Mathematics Software Science Sichuan Normal University Chengdu P.R.China 《应用数学和力学(英文版)》2007,(12)
First,the notions of the measure of noncompactnees and condensing set- valued mappings are introduced in locally FC-uniform spaces without convexity struc- ture.A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces.As applications, some new equilibrium existence theorems of generalized game involving condensing map- pings are established in locally FC-uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper. 相似文献