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1.
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
2.
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
3.
丁协平 《应用数学和力学(英文版)》1998,19(6):521-529
I.IntroductionLetDbeanonemptyconvexsubsetofaBanachspaceB,BbethetopologicaldualspaceofBand(u,v)bethepairingbetweenneBandr6B.LetT,A:D~B'and9:DxD-Bbethreemappingsandf:D~(-ac, ac1beareal-valuedfunction.Inthispaper,weshallinvestigatethemixednonlinearvariationalinequalityproblemMNna(T,A,9,f,D):FinduEDsuchthatSpecialCases.(l)f-0,thentheproblem(l.l)isequivalenttofindingueDsuchthatTheproblem(l.2)isthestronglynonlinearvariational-likeinequalityproblemstudiedbyNoorllJwhicharisesnaturallyincon… 相似文献
4.
张石生 《应用数学和力学(英文版)》2002,23(4):394-408
1 IntroductionandPreliminariesThroughoutthispaper,weassumethatEisarealBanachspace ,E isthetopologicaldualspaceofE ;〈· ,·〉isthedualpairbetweenEandE ,D(T) ,R(T) ,N(T) ,F(T)denotethedomainofT ,rangeofT ,thesetofallzeropointsofTandthesetofallfixedpointsofTrespectively… 相似文献
5.
张石生 《应用数学和力学(英文版)》2004,25(6)
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces.By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established.The results generalize,improve and unify a number of Noor's and others' recent results. 相似文献
6.
丁协平 《应用数学和力学(英文版)》2013,34(1):113-126
A new system of generalized mixed implicit equilibrium problems(SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces.First,an auxiliary mixed equilibrium problem(AMEP) is introduced.The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions.Next,by using the solution mapping of the AMEP,a system of generalized equation problems(SGEP) is considered,and its equivalence with the SGMIEP is shown.By using the SGEP,a new iterative algorithm for solving the SGMIEP is proposed and analyzed.The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions.These results are new,which unify and generalize some recent results in this field. 相似文献
7.
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
8.
刘英 《应用数学和力学(英文版)》2009,30(7):925-932
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others. 相似文献
9.
MULTI-VALUED QUASI VARIATIONAL INCLUSIONS IN BANACH SPACES 总被引:1,自引:0,他引:1
ZHANGShi-sheng 《应用数学和力学(英文版)》2004,25(6):627-635
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces. By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established. The results generalize, improve and unify a number of Noor‘s and others‘ recent results. 相似文献
10.
UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION 总被引:1,自引:0,他引:1
曾六川 《应用数学和力学(英文版)》2005,26(9):1204-1211
The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich' s open question is given. The results presented extend and improve Zhang Shisheng' s recent ones in the following aspects : (i) Zhang' s stronger condition that the sequence of iterative parameters converges to zero is removed; (ii) Zhang' s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; (iii) Zhang' s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann. 相似文献
11.
丁协平 《应用数学和力学(英文版)》2010,31(9):1049-1062
A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field. 相似文献
12.
The purpose of this paper is to study the almost sure T -stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of φ-weakly contractive type random operators in a separable Banach space.Under suitable conditions,the Bochner integrability of random fixed points for this kind of random operators and the almost sure T -stability and convergence for these two kinds of random iterative algorithms are proved. 相似文献
13.
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
14.
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
15.
曾六川 《应用数学和力学(英文版)》2003,24(12):1421-1430
IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E →2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉=‖x‖·‖f‖,‖f‖=‖x‖, x∈E . Definition 1 LetT :D →Dbeamapping .1 )Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞)withlimn→∞kn =1suchthat ‖Tnx-Tny‖≤kn‖x-y‖forall x ,y∈D ,n≥0 ;(1 ) 2 )Tissaidtobeofasymptoticallynonexpansivetype[2 ],if lims… 相似文献
16.
A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces. 相似文献
17.
REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES 总被引:2,自引:0,他引:2
1 IntroductionandPreliminariesSupposeEisarealBanachspaceandTisaselfmapofE .Supposex0 ∈Eandxn+1=f(T ,xn)definesaniterationprocedurewhichyieldsasequenceofpoints xn ∞n=0 inE .Foranexample ,thefunctioniterationxn+1=f(T ,xn) =Tx0 .SupposeF(T) =x∈E :Tx=x ≠ andthat xn convergess… 相似文献
18.
张石生 《应用数学和力学(英文版)》1999,20(6):585-592
The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative
processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this
paper extend and improve the corresponding results by Chang, Ding, Hassouni, Kazmi, Siddiqi, Zeng et al.
Foundation item: the National Natural Science Foundation of China (19771058) 相似文献
19.
张石生 《应用数学和力学(英文版)》2001,22(1):25-34
IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E → 2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉 =‖x‖·‖f‖ , ‖f‖ =‖x‖ (x∈E) . Ddfinition 1 1 LetT :D →Dbeamapping1 )Tissaidtobeasymptoticallyno… 相似文献
20.
张石生 《应用数学和力学(英文版)》2001,22(1)
Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained. 相似文献