On the convergence of solutions of inclusions containing maximal monotone and generalized pseudomonotone mappings

We are concerned in this paper with the existence, boundedness, and the convergence of solutions to a sequence of inclusions Ak(u)+Bk(u)∋Lk,Ak(u)+Bk(u)∋Lk, where AkAk is a maximal monotone mapping, BkBk is a generalized pseudomonotone mapping defined on a reflexive Banach space XX, and Lk∈X∗Lk∈X∗. We study appropriate kinds of convergence for AkAk and BkBk such that a limit of a sequence of solutions of these inclusions is also a solution of the limit inclusion.