A general framework for the over-relaxed A-proximal point algorithm and applications to inclusion problems

First, a general framework for the over-relaxed AA-proximal point algorithm based on the AA-maximal monotonicity is introduced, and second it is applied to the approximation solvability of a general class of nonlinear inclusion problems using the generalized resolvent operator technique. The over-relaxed AA-proximal point algorithm is of interest in the sense that it is quite application-oriented, but nontrivial in nature. The results obtained are general in nature.