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Non-convex hybrid algorithm for two families of quasi-Lipschitz mappings. (Chinese. English summary) Zbl 1399.47166

Summary: The purpose of this paper is to study iterative methods and proofs of strong convergence to common fixed points for two families of asymptotically quasi-Lipschitz mappings in Hilbert spaces. First, a kind of new non-convex hybrid algorithm 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 constructing convex and closed sets. The results presented here improve and extend the corresponding ones announced by many others.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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