Proximal point algorithms involving fixed point of nonspreading-type multivalued mappings in Hilbert spaces

Volume 9, Issue 10, pp 5561--5569 http://dx.doi.org/10.22436/jnsa.009.10.06

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Authors

Shih-Sen Chang - Center for General Educatin, China Medical University, Taichung 40402, Taiwan. Ding Ping Wu - School of Applied Mathematics, Chengdu University of Information Technology Chengsu, Sichuan 610103, China. Lin Wang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China. Gang Wang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China.

Abstract

In this paper, a new modified proximal point algorithm involving fixed point of nonspreading-type multivalued mappings in Hilbert spaces is proposed. Under suitable conditions, some weak convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the nonspreading-type multivalued mappings in Hilbert space are proved. The presented results in the paper are new.

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Keywords

• Convex minimization problem
• resolvent identity
• proximal point algorithm
• weak and strong convergence theorem
• nonspreading-type multivalued mapping.

MSC

•  47J05
•  47H09

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