A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

Shih-Sen Chang; Jen-Chih Yao; Ching-Feng Wen; Lin Wang

doi:10.1186/s13660-018-1825-5

A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

J Inequal Appl. 2018;2018(1):235. doi: 10.1186/s13660-018-1825-5. Epub 2018 Sep 12.

Authors

Shih-Sen Chang¹, Jen-Chih Yao¹, Ching-Feng Wen^{2

3}, Lin Wang⁴

Affiliations

¹ 1Center for General Education, China Medical University, Taichung, Taiwan.
² 2Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Taiwan.
³ 3Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, Taiwan.
⁴ 4College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China.

Abstract

The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.

Keywords: CAT(0) space; Hadamard space; Monotone mapping; Proximal point algorithm; Viscosity implicit approximation methods.