On Mann implicit composite subgradient extragradient methods for general systems of variational inequalities with hierarchical variational inequality constraints

Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote variational inequality problem, general system of inequalities, hierarchical inequality, common fixed-point problem countable family uniformly Lipschitzian pseudocontractive mappings an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-search process for finding solution CFPP, VIP. The suggested are based on iteration method, method process, viscosity approximation method. Under mild assumptions, we prove strong convergence to which solves certain HVI defined their solutions set.