The numerical reckoning of modified proximal point methods for minimization problems in non-positive curvature metric spaces

ABSTRACT

In this paper, we introduce a new modified proximal point algorithm for nonexpansive mappings in non-positive curvature metric spaces and also we prove the sequence generated by the proposed algorithms converges to a common solution between minimization problem and fixed point problem. Moreover, we give some numerical examples to illustrate our main results, that is, our algorithm is more efficient than the algorithm of Cholamjiak et al. and others.

KEYWORDS:

• CAT(0) spaces
• proximal point algorithm
• iterative method
• nonexapnsive mappings
• convex minimization problem

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 47H10
• 65K10
• 65K15

Acknowledgment

All authors contributed equally and significantly in writing this paper. The authors would to thanks the referees and Professor Jesus Vigo Aguiar for reading this paper carefully, providing valuable suggestions and comments, and pointing out a minor errors in the original version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Phatiphat Thounthong http://orcid.org/0000-0002-1453-4236

Nuttapol Pakkaranang http://orcid.org/0000-0002-0224-4661

Yeol Je Cho http://orcid.org/0000-0002-1250-2214

Wiyada Kumam http://orcid.org/0000-0001-8773-4821

Poom Kumam http://orcid.org/0000-0002-5463-4581

Additional information

Funding

The authors acknowledge the financial support provided by King Mongkut's University of Technology Thonburi through the ‘KMUTT 55th Anniversary Commemorative Fund’. Phatiphat Thounthong was financially supported by King Mongkut's University of Technology North Bangkok. Contract No. KMUTNB-61-GOV-D-68. Wiyada Kumam was financial supported by the Rajamangala University of Technology Thanyaburi (RMUTT). Furthermore, then project was supported by Theoretical and computation Science(TaCS) Center under Computational and Applied Science for Smart Innovation Research Cluster (CLASSIC), Faculty of Science, KMUTT.