Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Lu-Chuan Ceng, Xiaoye Yang
2019 Mathematics  
This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm
more » ... it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.
doi:10.3390/math7030218 fatcat:pwdrvscnzrb5tj4tcxf6sxglkq