"In this paper, we study a class of strongly nonlinear implicit complementarity problems in the setting of Hilbert spaces $H$ (not necessarily Hilbert lattices). By using the property of the projection and a suitable change of variables, we establish the equivalence between the strongly nonlinear implicit complementarity problem and the fixed point problem in $H$. Moreover, we use this equivalence and the fixed point theorem of Boyd and Wong to prove the existence and uniqueness of solutions for the strongly nonlinear implicit complementarity problem in $H$."

Keywords: Nonlinear implicit complementarity problem, projection, change of variables, fixed point theorem, Hilbert space