On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces

Abstract

We propose a new modified proximal point algorithm combined with Halpern's iteration process for nonexpansive mappings in the framework of CAT(0) spaces. We establish a strong convergence theorem under some mild conditions. Our results extend some known results which appeared in the literature.

Keywords:

• convex minimization problem
• fixed-point problem
• CAT(0) space
• proximal point algorithm
• nonexpansive mapping

AMS Subject Classification:

• 47H09
• 47H10

Acknowledgments

The authors would like to thank the referees for valuable comments and suggestions for improving this work. R. Suparatulatorn and P. Cholamjiak would like to thank University of Phayao.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Thailand Research Fund [Project: RTA5780007] and Chiang Mai University.