Shrinking Projection Methods for a Family of Quasi-$\phi$-Strict Asymptotically Pseudo-Contractions in Banach Spaces
Received:April 19, 2010  Revised:October 12, 2010
Key Word: strong convergence   a family of quasi-$\phi$-strict asymptotically pseudo-contractions   generalized projection   shrinking projection method   Banach spaces.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10771050) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No.11JK0486).
 Author Name Affiliation Xing Hui GAO College of Mathematics and Computer Science, Yan'an University, Shaanxi 716000, P. R. China Hai Yun ZHOU Department of Basic Courses, Shijiazhuang Mechanical Engineering College, Hebei 050003, P. R. China
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The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-$\phi$-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property (K). The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.