Convergence Analysis Monotone Hybrid Algorithms for Countable Family of Generalized Nonexpansive Mappings and Maximal Monotone Operators

Aibinu, Mathew; Moyo, Sibusiso

Convergence Analysis Monotone Hybrid Algorithms for Countable Family of Generalized Nonexpansive Mappings and Maximal Monotone Operators

Document Type : Original Article

Authors

Mathew Aibinu ¹^{, 2}
Sibusiso Moyo ³^{, 2}

¹ Institute for Systems Science and KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa.

² National Institute for Theoretical and Computational Sciences (NITheCS), South Africa.

³ Department of Applied Mathematics and School for Data Science and Computational Thinking, Stellenbosch University, South Africa.

Abstract

A new countable family of generalized nonexpansive mappings is introduced and a new monotone hybrid algorithm is presented in the framework of Banach spaces. Some new results are obtained for the class of generalized nonexpansive mappings and countable family of generalized nonexpansive mappings. The study exhibits the procedure for obtaining a common element of the zero point set of a maximal monotone operator and the newly introduced countable family of generalized nonexpansive mappings.

Keywords