对广义非线性隐拟变分包含的Mann和Ishikawa型摄动迭代算法  

MANN and ISHIKAWA Type Perturbed Algorithms for Generalzed Nonlinear Quasivariational Inclusion

作　　者：王庆先[1] 尚明生[2] 

机构地区：[1]云南师范大学数学系,云南昆明650092 [2]四川师范学院数学系,四川南充637002

出　　处：《云南师范大学学报（自然科学版）》2000年第1期9-14,共6页Journal of Yunnan Normal University:Natural Sciences Edition

摘　　要：本文研究了一类较一般化的变分包含: 0∈N(w ,y) + M((g - m )(u),u).它包含了近几年丁协平,黄南京,M.A.Noor等作者所作的变分包含问题。在实Hilbert空间中,我们利用极大单调算子的性质,证明了它和不动点问题间的等价性,其解的存在性和由算法产生的近似解的收敛性。我们的结果改进和推广了最近许多文章中相应的算法和结果。This paper studied a new generalized variational inclusions : 0∈N(w,y)+ M((g-m)(u),u),which include many variational inclusions studied by X.P.Ding, N.J.Huang and M.A.Noor and so on in recent years.Using the resolvent technique, we establish the equivalence between the generalized nonlinear quasivariational inclu- sions and the fixed point problem, and prove the existence of its solution and the convergence of its proximate solution generated by ITPIA in real Hilbert space. Our results improved and generalized many known corresponding algorithms and results.

关 键 词：非线性 变分包含 集值算子 摄动迭代算法 MTPIA 

分 类 号：O177.91[理学—数学]