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

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,Plubtieng 等,Colao等,Yao等及其他人的一些最新的结果．

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

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 common 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, 71:27082715], Plubtieng, et al J Math Anal Appl,2007, 336:455-469],Colao, et al J Math Anal Appl, 2008, 344:340-352],Yao, et al Fixed Point Theory Appl,2007, Art ID64363] and others.