Generalized nonlinear variational-like inequalities in reflexive Banach spaces

In this paper, we introduce and study a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By applying the auxiliary principle technique due to Glowinski-Lions-Tremolieres (Ref. 1) and the minimax inequality due to Ding-Tan (Ref. 2), we establish existence and uniqueness theorems for solutions of generalized nonlinear variational-like inequalities; also, we suggest two general algorithms and prove the convergence of the iterative sequences generated by the algorithms. Our results extend, improve, and unify several known results due to Cohen, Ding, Bose, Parida-Sahoo-Kumar, Dien, Ding-Tarafdar, Noor, and others.