On a Hybrid Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of a Family of Quasi--Asymptotically Nonexpansive Mappings in Banach Spaces
On a Hybrid Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of a Family of Quasi--Asymptotically Nonexpansive Mappings in Banach Spaces
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DOI：
10.1155/2010/157278
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发表时间：
2010-02
影响因子：
--
通讯作者：
Min Liu;Shih-sen Chang;Ping Zuo
中科院分区：
文献类型：
--
作者：
Min Liu;Shih-sen Chang;Ping Zuo
在严格凸自反Banach空间中，利用混合方法寻找广义混合平衡问题解的公共元素、一族拟渐近非扩张映象的不动点集以及在较弱条件下的Fréchet可微范数，证明了一个强收敛定理.证明的方法不同于S.Takahashi和W.Takahashi(2008)以及Takahashi和Zembayashi(2008)的证明方法，见参考文献。它还表明，迭代方法中使用的投影类型与映射的性质无关。文中的结果改进和推广了最近的一些结果。
We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi--asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Fréchet differentiable norm under weaker conditions. The method of the proof is different from, S. Takahashi and W. Takahashi that by (2008) and that by Takahashi and Zembayashi (2008) and see references. It also shows that the type of projection used in the iterative method is independent of the properties of the mappings. The results presented in the paper improve and extend some recent results.