A note on Solodov and Tseng’s methods for maximal monotone mappings

This paper considers the problem of finding a zero of the sum of a single-valued Lipschitz continuous mapping AA and a maximal monotone mapping BB in a closed convex set CC. We first give some projection-type methods and extend a modified projection method proposed by Solodov and Tseng for the special case of B=NCB=NC to this problem, then we give a refinement of Tseng’s method that replaces PCPC by PCkPCk. Finally, convergence of these methods is established.