Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings

In real Hilbert spaces, let the CFPP indicate a common fixed-point problem of asymptotically nonexpansive operator and countably many operators, suppose that HVI VIP represent hierarchical variational inequality problem, respectively. We put forward Mann hybrid deepest-descent extragradient approach for solving with constraints. The proposed algorithms are on basis Mann’s iterative technique, viscosity approximation method, subgradient rule linear-search process, rule. Under suitable restrictions, it is shown sequences constructed by converge strongly to solution