关于两族拟Lipschitz映像的非凸混杂算法

Non-convex Hybrid Algorithm for Two Families of Quasi-Lipschitz Mappings

【目的】研究两族渐近拟Lipschitz映像的公共不动点的迭代方法以及强收敛性的证明。【方法】利用构造凸闭集的方法和投影算子的定义和性质等技巧。【结果】首先,在Hilbert空间中,构造出一种新的关于两族渐近拟Lipschitz映像的公共不动点的非凸混杂投影算法,其次,利用构造凸闭集的方法证明了该算法的强收敛性。【结论】所得结论是最新文献相关结论之推广。

[Purposes]The purpose is to study itarative methods and proofs of strong convergence of common fixed points for two families of asymptotically quasi-Lipschitz mappings in Hilbert spaces.The strong convergence of the proposed algorithm is proved by the method of constructing concex and closed sets.The results presented here improve and extend the corresponding ones announced by many others.[Methods]The method of constructing concex and closed sets and the definition and properties of projective operator are used.[Findings]First,a kind of new non-convex hybrid algorithms of common fixed points is established for two families of asymptotically quasi-Lipschitz mappings in Hilbert spaces.Second,the strong convergence of the proposed algorithm is proved by the method of constructing concex and closed sets.[Conclusions]The results presented here improve and extend the corresponding ones announced by many others.