Quasi-mildly Nonlinear Complementarity Problems of the Set-Valued Mappings

We consider the following quasi-mildly nonlinear complementarity problems for set-valued mappings: to find x ∈ k(x), y ∈ V(x), such that Mx + q + Ay ∈ k*(x),〈x − m(x), Mx + q + Ay〉 = 0. First, we construct a new iterative algorithm to compute the approximate solution for this problem. Then, by application of this algorithm, an existence theorem is obtained by the authors, so that a series of results of M. A. Noor, J. S. Pang, and C. E. Lemke are generalized.