On Solvability of a Generalized Nonlinear Variational-Like Inequality

Abstract

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like inequality. The convergence of the sequence generated by the iterative algorithm is also discussed.