Convergence analysis of modified Picard-S hybrid iterative algorithms for total asymptotically nonexpansive mappings in Hadamard spaces

ABSTRACT

In this paper, we introduce new type iterative scheme called a ‘modified Picard-S hybrid’ iterative algorithm to establish Δ-convergence and strong convergence theorems under suitable conditions for total asymptotically nonexpansive mappings in CAT(0) spaces. Our results in the paper improve and extend many results appeared in the literature. Moreover, we also illustrate numerical examples for the proposed iteration process to compare speed of convergence among the existing iterative algorithms.

KEYWORDS:

• Total asymptotically nonexpansive mappings
• modified Picard-S hybrid iteration
• modified Picard-Ishikawa hybrid iteration
• CAT(0) spaces

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 47H10

Acknowledgements

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

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

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

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’. Wiyada Kumam was financial supported by the Rajamangala University of Technology Thanyaburi (RMUTTT). Prasit Cholamjiak thanks School of Science, University of Phayao. Furthermore, this project was supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation Research Cluster (CLASSIC), Faculty of Science, KMUTT.