Fixed point theorem and nonlinear complementarity problem in Hilbert spaces
Hongjun Wang, Yuchun Zheng · The Journal of Nonlinear Sciences and Applications · 2016
In this paper, the concept of the strongly monotone type mapping is introduced, which contains the strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence between the fixed point problem and the complementarity problem of strongly monotone type mapping. Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution of such a nonlinear complementarity problem on the proper conditions. The error estimation of such an iteration is discussed.