OICC Press Communications in Nonlinear Analysis 2371-7920 11 2 2025 11 09 A monotone hybrid algorithm for maximal monotone operators and a family of generalized nonexpansive mappings EN Mathew Aibinu Institute for Systems Science & KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa. DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), South Africa 0000-0003-4901-1440 Journal Article 2025 11 09 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.