Convergence of Thakur Iteration Scheme for Mean Nonexpansive Mappings in Hyperbolic Spaces

Sahu, Omprakash; Banerjee, Amitabh

doi:10.21608/ejmaa.2024.268222.1126

Convergence of Thakur Iteration Scheme for Mean Nonexpansive Mappings in Hyperbolic Spaces

Document Type : Regular research papers

Authors

Omprakash Sahu ¹
Amitabh Banerjee ²

¹ Mathematics, Babu Pandhri Rao Kridatt Govt. College Silouti

² Principal, Govt. J. Y. Chhattisgarh College Raipur, India

10.21608/ejmaa.2024.268222.1126

Abstract

The purpose of this paper, we modify the Thakur iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish strong and $\Delta$- convergence theorems for mean nonexpansive mappings in uniformly convex hyperbolic spaces. We provide an example of mean nonexpansive mapping which is not nonexpansive mapping. Using this example and some numerical texts, we infer empirically that the Thakur iteration process converges faster than the Abbas, Agarwal, Noor, Ishikawa, and Mann iteration processes.
The purpose of this paper, we modify the Thakur iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish strong and $\Delta$- convergence theorems for mean nonexpansive mappings in uniformly convex hyperbolic spaces. We provide an example of mean nonexpansive mapping which is not nonexpansive mapping. Using this example and some numerical texts, we infer empirically that the Thakur iteration process converges faster than the Abbas, Agarwal, Noor, Ishikawa and Mann iteration process.

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