Convergence theorems by monotone hybrid algorithms for a family of generalized nonexpansive mappings and maximal monotone operators
نویسندگان
1 Institute for Systems Science and KZN e-Skills CoLab, Durban University of Technology, South Africa
2 DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa
doi
10.22075/ijnaa.2023.29593.4201چکیده
Finding a zero of a maximal monotone operator is known as one of the most impressive problems which are associated with convex analysis and mathematical optimization. Akin to this is solving the fixed point problems of the class of nonexpansive mappings, which constitutes an important part of nonlinear operators with fascinating applications in several areas such as signal processing and image restoration. This study presents a monotone hybrid algorithm for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a family of a generalized nonexpansive mapping in a Banach space. Suitable conditions under which the algorithm converges strongly are established.
