New approach to the η-proximal point algorithm and nonlinear variational inclusion problems

A new approach using the over-relaxed proximal point algorithm in the context of solving a class of inclusion problems based on the notion of maximal (η)-monotonicity is developed and examined. Convergence analysis seems to be reasonable, and finally, some specializations are included. Furthermore, the model developed in this communication seems to be appropriate to the Yosida approximation in the sense that it can be applied to first-order evolution equations/inclusions as well.