A monotone hybrid algorithm for maximal monotone operators and a family of generalized nonexpansive mappings

Aibinu, Mathew

A monotone hybrid algorithm for maximal monotone operators and a family of 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

In this paper, a new monotone hybrid method is introduced in the framework of Banach spaces for finding a common element of the set of zeros of a maximum monotone operator and the fixed point set of a family of generalized nonexpansive mappings. The prove is given in the framework of Banach spaces for the strong convergence of a sequence of iteration to a common element of the set of zeros of a maximum monotone operator and the fixed point set of a family of generalized nonexpansive mappings. New convergence results are obtained for resolvents of maximal monotone operators and a family of generalized nonexpansive mappings in a Banach space.

Keywords