Relaxed and hybrid viscosity methods for general system of variational inequalities with split feasibility problem constraint
Lu-Chuan Ceng, Jen‐Chih Yao · Fixed Point Theory and Applications · 2013
In this paper, we propose and analyze some relaxed and hybrid viscosity iterative algorithms for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of infinite-dimensional Hilbert spaces.We prove that the sequences generated by the proposed algorithms converge strongly to an element of Fix(S) ∩ Ξ ∩ Γ under mild conditions.