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Zbl 1187.47045
Chang, Shih-Sen; Kim, Jong Kyu; Wang, Xiong Rui
Modified block iterative algorithm for solving convex feasibility problems in Banach spaces. (English)
[J] J. Inequal. Appl. 2010, Article ID 869684, 14 p. (2010). ISSN 1029-242X/e

Summary: The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-$\varphi $-asymptotically nonexpansive mappings. Under suitable conditions, some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with the Kadec-Klee property. The results presented in the paper improve and extend some recent results.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties

Keywords: modified block iterative method; convex feasibility problems; quasi-$\varphi $-asymptotically nonexpansive mappings; strong convergence; uniformly smooth; Banach spaces

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