F-Implicit Complementarity Problems in Banach Spaces

Abstract

The F-implicit complementarity problem (F-ICP) and F-implicit variational inequality problem (F-IVIP) are introduced and studied. The equivalence between (F-ICP) and (F-IVIP) is presented under certain assumptions. Furthermore, we derive some new existence theorems of solutions for (F-ICP) and (F-IVIP) by using the Fan–Knaster–Kuratowski–Mazurkiewicz Math. Ann. 142 (1961), 305–310] and Lin's Bull. Austral. Math. Soc. 34 (1986), 107–117] under some suitable assumptions without the monotonicity.