System of Set-Valued Nonlinear Generalized Variational Inclusion Problems in Banach Spaces (Journal of Mathematical Study, 2023)
In this paper, we consider a system of set-valued nonlinear generalized variational inclusion problems (SNGVIP) in $q$-uniformly smooth Banach spaces. We definea class of $H(·,·)$-mixed mappings and its associated class of resolvent operators. Further, using proximal-point mapping method, we suggest an iterative algorithm forfinding the solution of the system of set-valued nonlinear generalized variational inclusion problems. Furthermore, we discuss the convergence criteria of the sequencesgenerated by the iterative algorithm.
Keywords: System of set-valued nonlinear generalized variational inclusion problems; $H(·; ·)$-mixed mappings; proximal-point mapping; $q$-uniformly smooth Banach spaces; convergence analysis.