Proximal Point Algorithms Involving Cesàro Type Mean of Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Volume 9, Issue 6, pp 4317--4328 http://dx.doi.org/10.22436/jnsa.009.06.73

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Authors

Shih-Sen Chang - Center for General Educatin, China Medical University, Taichung, 40402, Taiwan. Ching-Feng Wen - Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan. Jen-Chih Yao - Center for General Educatin, China Medical University, Taichung, 40402, Taiwan. - Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan.

Abstract

In this paper, a new modified proximal point algorithm involving fixed point of Cesàro type mean of asymptotically nonexpansive mappings in CAT(0) spaces is proposed. We also introduce a new iterative scheme. Under suitable conditions, the \(\Delta\)-convergence and the strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the Cesàro type mean of asymptotically nonexpansive mapping in CAT(0) space are proved. The results presented in the paper are new.

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Keywords

• Convex minimization problem
• resolvent identity
• CAT(0) space
• proximal point algorithm
• asymptotically nonexpansive mapping.

MSC

•  47H09
•  47H10
•  47J25
•  90C33

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