摘要
在Hilbert空间,讨论了一类广义非线性变分不等式组解的存在性及迭代逼近,并做了相应的收敛性分析.所得结果推广和改进了目前一些文献只讨论包含一个非线性算子的变分不等式组以及提出算法是隐式的结果.
The existence of solution and iterative approximation for a system of generalized nonlinear variational inequalities in Hilbert space was discussed. And the convergence analysis of this system was shown. The result extends some documents which study the system of variational inequalities including only one nonlinear operator and also improves the result to show the method is implicit.
引文
[1]VERMA R U.Projection methods,algorithms,and a new system of nonlinear variational inequalities[J].Comput Math Appl,2001,41(7):1025-1031.
[2]罗元松.Hilbert空间中一般形式的松弛余强制变分不等方程组解的迭代逼近问题[J].四川大学学报(自然科学版),2007,44(3):467-471.
[3]曹寒问.一类新广义非线性似变分不等式组解的迭代逼近[J].南昌大学学报(自然科学版),2010,34(3):221-226.
[4]HASSOUNI A,MOUDAFI A.A perturbed algorithms for variational inclusions[J].J Math Anal Appl,1994,185(3):706-721.
[5]MOHAPATRA R N,VERMA R U.Sensitivity analysis for cocoercively monotone variational inclusions and(A,η)maximal monotonicity[J].J Appl Math Comp,2008,26(1-2):281-293.
[6]BREZIS H.Operateurs Maximaux Monontone et Semigroups de Contractions dans les Espaces de Hilbert[M].Amsterdam:North-Holland,1973.
[7]彭再云,雷鸣,汪达成,等.希尔伯特空间中的广义松弛余强制变分不等式体系及带误差的三步投影方法[J].四川师范大学(自然科学版),2009,32(2):168-171.