不动点问题平衡问题及变分不等式问题的具弱压缩的粘性逼近  

Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem

作　　者：张石生[1] 李向荣[2] 陈志坚[2] 柳京爱[3] 

机构地区：[1]宜宾学院数学系,四川宜宾644007 [2]香港理工大学应用数学系 [3]北京石油化工学院数理系,北京102617

出　　处：《应用数学和力学》2010年第10期1211-1219,共9页Applied Mathematics and Mechanics

摘　　要：借助具弱压缩的粘性逼近,提出一种新的修正的迭代算法,用以寻求一公共元,它既是一无穷族非扩张映像的公共不动点集中的点,也是一有限族的平衡问题的解集中的点,而且它还是一变分不等式的解.在适当的条件下,一些强收敛定理在Hilbert空间的框架下被建立.所得结果推广和改进了Colao等[Nonlinear Anal,2009,71:2708-2715],Plubtieng等[JMath Anal Appl,2007,336:455-469],Colao等[JMath Anal Appl,2008,344:340-352],Yao等[Fixed Point Theory Appl,2007,ArtID64363]及其他人的一些最新的结果.The purpose was by using the viscosity approximation method with a weak contraction to propose a modified iterative algorithm for finding a common element of the set of com- mon fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems which was also a solution of a variational inequality. Under suitable conditions, some strong convergence theorems were established in the framework of Hilbert spaces. The results presented improve and extend the corresponding results in Colao, et al [Nonlinear Anal, 2009,71： 2708-2715], Plubtieng, et a/[J Math Anal Appl, 2007, 335： 455- 459 j, Colao, et al[ J Math Anal Appl, 2008, 344 ： 340-352 ], Yao, et al[ Fixed Point Theory Ap- pl,2007, Art ID 54353 ] and others.

关 键 词：具弱压缩映像的粘性逼近 平衡问题 非扩张映像 隐迭代 极小化问题 

分 类 号：O177.91[理学—数学]