Banach空间中关于广义变分不等式的杂交投影算法
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摘要
本文利用杂交广义投影算法引进了一迭代序列来逼近Banach空间中一类广义变分不等式的解.因为这类广义变分不等式包括古典变分不等式和相补问题作为特殊例子,因此本文统一了以前一些相关结果.
In this paper,we introduce an iterative sequence by using the hybrid generalized projection algorithm for approximating a solution of a general variational inequality in Banach spaces.Since the general variational inequality includes the classical variational inequality and complementarity problem as special cases,results obtained in this paper unify some previous corresponding results.
In this paper,we introduce an iterative sequence by using the hybrid generalized projection algorithm for approximating a solution of a general variational inequality in Banach spaces.Since the general variational inequality includes the classical variational inequality and complementarity problem as special cases,results obtained in this paper unify some previous corresponding results.
引文
[1]Noor M A.General variational inequalities.Appl.Math.Lett.,1988,1:119-121
[2]Noor M A.General variational inequalities and nonexpansive mappings.J.Math.Anal.Appl.,2007,331:810-822
[3]Noor M A.Merit functions for general variational inequalities.J.Math.Anal.Appl.,2006,316:736-752
[4]Noor M A.New approximation schemes for general variational inequalities.J.Math.Anal.Appl.,2000,251:271-229
[5]Noor M A.New extragradient-type methods for general variational inequalities.J.Math.Anal.Appl.,2003,277:379-395
[6]Noor M A.Some developments in general variational inequalities.Appl.Math.Comput.,2004,152:199-277
[7]Noor M A.Wiener-Hopf equations and variational inequalities.J.Optim.Theory Appl.,1993,79:197-206
[8]Noor M A,Huang Z.Three-step iterative methods for nonexpansive mappings and variational inequalities.Appl.Math.Comput.,2007,187:680-685
[9]Alber Ya.Metric and generalized projection operators in Banach spaces:properties and applications.In:Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type,ed.by A.Kartsatos,Marcel Dekker,New York,1996,15-50
[10]Iiduka H,Takahashi W.Strong convergence theorems for nonexpan-sive mappings and inverse-strongly monotone mappings.Nonlinear Analysis,2005,61:341-350
[11]Iiduka H,Takahashi W.Weak convergence of a projection algorithm for variational inequalities in a Banach space.J.Math.Anal.Appl,2008,339:668-679
[12]Liu Y.Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space.Applied Mathematics and Mechanics(English Edition),2009,30:925-932
[13]Liu Y.Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings.J.Glob.Optim.,2010,46:319-329
[14]Matsushita S,Takahashi W.A strong convergence theorem for relatively nonexpansive mappings in a Banach space.Journal of Approximation Theory,2005,134:257-266
[15]Browder F E,Petryshyn W V.Construction of fixed points of nonlinear mappings in Hilbert space.J.Math.Anal.Appl.,1967,20:197-228
[16]Iiduka H,Takahashi W,Toyoda M.Approximation of solutions of variational inequalities for monotone mappings.Panamer.Math.J.,2004,14:49-61
[17]Liu F,Nashed M Z.Regularization of nonlinear ill-posed variational inequalities and convergence rates.Set-Valued Anal.,1998,6:313-344
[18]Noor M A.Extended general variational inequalities.Appl.Math.Lett.,2009,22:182-186
[19]Noor M A.Projection iterative methods for extended general variational inequalities.J.Appl.Math.Corn-put.,2010,32:83-95
[20]Noor M A,Noor K I.Sensitivity analysis of some quasi variational inequalities.J.Adv.Math.Stud.,2013,6:43-52
[21]Noor,M A,Noor K I,Khan A G.Some iterative schemes for solving extended general quasi variational inequalities.Appl.Math.Inf.Sci.,2013,7(3):917-925
[2]Noor M A.General variational inequalities and nonexpansive mappings.J.Math.Anal.Appl.,2007,331:810-822
[3]Noor M A.Merit functions for general variational inequalities.J.Math.Anal.Appl.,2006,316:736-752
[4]Noor M A.New approximation schemes for general variational inequalities.J.Math.Anal.Appl.,2000,251:271-229
[5]Noor M A.New extragradient-type methods for general variational inequalities.J.Math.Anal.Appl.,2003,277:379-395
[6]Noor M A.Some developments in general variational inequalities.Appl.Math.Comput.,2004,152:199-277
[7]Noor M A.Wiener-Hopf equations and variational inequalities.J.Optim.Theory Appl.,1993,79:197-206
[8]Noor M A,Huang Z.Three-step iterative methods for nonexpansive mappings and variational inequalities.Appl.Math.Comput.,2007,187:680-685
[9]Alber Ya.Metric and generalized projection operators in Banach spaces:properties and applications.In:Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type,ed.by A.Kartsatos,Marcel Dekker,New York,1996,15-50
[10]Iiduka H,Takahashi W.Strong convergence theorems for nonexpan-sive mappings and inverse-strongly monotone mappings.Nonlinear Analysis,2005,61:341-350
[11]Iiduka H,Takahashi W.Weak convergence of a projection algorithm for variational inequalities in a Banach space.J.Math.Anal.Appl,2008,339:668-679
[12]Liu Y.Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space.Applied Mathematics and Mechanics(English Edition),2009,30:925-932
[13]Liu Y.Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings.J.Glob.Optim.,2010,46:319-329
[14]Matsushita S,Takahashi W.A strong convergence theorem for relatively nonexpansive mappings in a Banach space.Journal of Approximation Theory,2005,134:257-266
[15]Browder F E,Petryshyn W V.Construction of fixed points of nonlinear mappings in Hilbert space.J.Math.Anal.Appl.,1967,20:197-228
[16]Iiduka H,Takahashi W,Toyoda M.Approximation of solutions of variational inequalities for monotone mappings.Panamer.Math.J.,2004,14:49-61
[17]Liu F,Nashed M Z.Regularization of nonlinear ill-posed variational inequalities and convergence rates.Set-Valued Anal.,1998,6:313-344
[18]Noor M A.Extended general variational inequalities.Appl.Math.Lett.,2009,22:182-186
[19]Noor M A.Projection iterative methods for extended general variational inequalities.J.Appl.Math.Corn-put.,2010,32:83-95
[20]Noor M A,Noor K I.Sensitivity analysis of some quasi variational inequalities.J.Adv.Math.Stud.,2013,6:43-52
[21]Noor,M A,Noor K I,Khan A G.Some iterative schemes for solving extended general quasi variational inequalities.Appl.Math.Inf.Sci.,2013,7(3):917-925