Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space

ABSTRACT

In this paper, we establish strong and Δ-convergence theorems of the modified hybrid-CR three steps iteration with perturbations for total asymptotically non-expansive mapping in $\mathrm{CAT}(0)$ spaces. Our results improve and extend the corresponding results from the current literature. We also provide three examples to illustrate the convergence behaviour of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes.

KEYWORDS:

• Fixed point
• $\mathrm{CAT}(0)$ spaces
• three steps iteration
• hybrid iteration
• perturbations

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47J25
• 47H09

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Kenyi Calderón http://orcid.org/0000-0001-5361-3351

J. Martínez-Moreno http://orcid.org/0000-0002-3340-2781

E. M. Rojas http://orcid.org/0000-0002-8593-0463