Convergence theorems for some multi-valued generalized nonexpansive mappings

In this paper, we propose an algorithms for finding a common fixed point of an infinite family of multi-valued generalized nonexpansive mappings in uniformly convex Banach spaces. Under suitable conditions some strong and weak convergence theorems for such mappings are proved. The results presented...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering 2014-02, Vol.2014 (1), p.1-11, Article 33
Main Authors: Chang, Shih-sen, Tang, Yong-kun, Wang, Lin, Xu, Yu-guang, Zhao, Yun-he, Wang, Gang
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Banach space
Convergence
Differential Geometry
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Theorems
Topology
Variational Analysis and Fixed Point Theory
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Summary:In this paper, we propose an algorithms for finding a common fixed point of an infinite family of multi-valued generalized nonexpansive mappings in uniformly convex Banach spaces. Under suitable conditions some strong and weak convergence theorems for such mappings are proved. The results presented in the paper improve and extend the corresponding results of Suzuki (J. Math. Anal. Appl. 340:1088-1095, 2008), Eslamian and Abkar (Math. Comput. Model. 54:105-111, 2011), Abbas et al. (Appl. Math. Lett. 24:97-102, 2011) and others. MSC: 47J05, 47H09, 49J25.
ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/1687-1812-2014-33