Strong Convergence of Monotone Hybrid Algorithms for Maximal Monotone Mappings and Generalized Nonexpansive Mappings

Aibinu, Mathew

Strong Convergence of Monotone Hybrid Algorithms for Maximal Monotone Mappings and Generalized Nonexpansive Mappings

Document Type : Original Article

Author

Mathew Aibinu ¹^{, 2}^{, 3}

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

² DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa.

³ National Institute for Theoretical and Computational Sciences (NITheCS), South Africa

Abstract

A class of generalized nonexpansive mappings in Banach spaces is considered and a new monotone hybrid algorithm is presented for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping. Under certain conditions on the associated parameters, a strong convergence result is established. Moreover, the obtained result is applied to prove a strong convergence theorem for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping in a Hilbert space.

Keywords