无穷个m增生映射公共零点和变分不等式解的杂交迭代算法及计算试验（英文）
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摘要
本文设计一种新的杂交迭代算法用以逼近变分不等式的解集和两组无穷个m增生映射零点集的公共元.充分利用距离投影映射和豫解式算子的性质,证明一个强收敛定理.利用Visual Basic 6编程,通过计算机运算,验证迭代算法的有效性.本文把有限个算子的研究推广到无限个算子的情形并把抽象理论与计算机编程结合在一起,推广和补充了近期的相关研究工作.
One new hybrid iterative scheme for approximating the common element of the set of the solutions of variational inequalities and the sets of zeros of two infinite families of m-accretive mappings is presented. A strong convergence theorem is proved by using the properties of metric projection and resolvent sufficiently. The computational experiment to demonstrate the effectiveness of the proposed iterative schemes by using the codes of Visual Basic Six are conducted. The results in this paper extend the case of finite mappings to that of infinite mappings and combine the abstract results and the knowledge of computer programming, which extend and complement some of the recent corresponding work.
One new hybrid iterative scheme for approximating the common element of the set of the solutions of variational inequalities and the sets of zeros of two infinite families of m-accretive mappings is presented. A strong convergence theorem is proved by using the properties of metric projection and resolvent sufficiently. The computational experiment to demonstrate the effectiveness of the proposed iterative schemes by using the codes of Visual Basic Six are conducted. The results in this paper extend the case of finite mappings to that of infinite mappings and combine the abstract results and the knowledge of computer programming, which extend and complement some of the recent corresponding work.
引文
[1]Radon J.Theorie und Anwendungen der abolut additiven Mengenfunctionen[J].Sitz.Akad.Wiss.Wien.,1913,122:1295-1438.
[2]WEI Li,TAN Ruilin.Strong and weak convergence theorems for common zeros of finite accretive mappings[J].Fixed Point Theory Appl.,2014,Article ID 77.
[3]WEI Li,Agarwal R P.Iterative algorithms for infinite accretive mappings and applications to pLaplacian-like differential systems[J].Fixed Point Theory Appl.,2016,Article ID 5.
[4]Takahashi W.Nonlinear Functional Analysis[M].Yokohama:Yokohama Publishers,2000.
[5]Bruck R E.Properties of fixed-point sets of nonexpansive mappings in Banach spaces[J].Trans.Am.Math.Soc.,1973,179:251-262.
[6]Rockafellar R T.On the maximality of sums of nonlinear monotone operators[J].Trans.Am.Math.Soc.,1970,149:75-88.
[7]Zegeye H,Shahzad N.Strong convergence theorems for a common zero of a finite family of m-accretive mappings[J].Nonli.Anal.,2007,66:1161-1169.
[8]HU L G,LIU L W.A new iterative algorithm for common solutions of a finite family of accretive operators[J].Nonli.Anal.,2009,70:2344-2351.
[9]QIU Y P,CENG L C,CHEN J Z,HU H Y.Hybrid iterative algorithms for two families of finite maximal monotone mappings[J].Fixed Point Theory Appl.,2015,Article ID 180.
[10]WEI Li,ZHOU Haiyun.Modified hybrid iterative schemes for fixed points of relatively nonexpansive mappings and their applications[J].Mathematica Applicata,2009,22(3):624-630.
[11]WANG SH,ZHANG P.Some results on an infinite family of accretive operators in a reflexive Banach space[J].Fixed Point Theory Appl.,2015,Article ID 8.
[2]WEI Li,TAN Ruilin.Strong and weak convergence theorems for common zeros of finite accretive mappings[J].Fixed Point Theory Appl.,2014,Article ID 77.
[3]WEI Li,Agarwal R P.Iterative algorithms for infinite accretive mappings and applications to pLaplacian-like differential systems[J].Fixed Point Theory Appl.,2016,Article ID 5.
[4]Takahashi W.Nonlinear Functional Analysis[M].Yokohama:Yokohama Publishers,2000.
[5]Bruck R E.Properties of fixed-point sets of nonexpansive mappings in Banach spaces[J].Trans.Am.Math.Soc.,1973,179:251-262.
[6]Rockafellar R T.On the maximality of sums of nonlinear monotone operators[J].Trans.Am.Math.Soc.,1970,149:75-88.
[7]Zegeye H,Shahzad N.Strong convergence theorems for a common zero of a finite family of m-accretive mappings[J].Nonli.Anal.,2007,66:1161-1169.
[8]HU L G,LIU L W.A new iterative algorithm for common solutions of a finite family of accretive operators[J].Nonli.Anal.,2009,70:2344-2351.
[9]QIU Y P,CENG L C,CHEN J Z,HU H Y.Hybrid iterative algorithms for two families of finite maximal monotone mappings[J].Fixed Point Theory Appl.,2015,Article ID 180.
[10]WEI Li,ZHOU Haiyun.Modified hybrid iterative schemes for fixed points of relatively nonexpansive mappings and their applications[J].Mathematica Applicata,2009,22(3):624-630.
[11]WANG SH,ZHANG P.Some results on an infinite family of accretive operators in a reflexive Banach space[J].Fixed Point Theory Appl.,2015,Article ID 8.