Communications of the
Korean Mathematical Society CKMS

General framework for proximal point algorithms based on the notion of $(A,\eta)$-maximal monotonicity (also referred to as $(A,\eta)$-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to $(A,\eta)$-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

Keywords: variational inclusions, maximal monotone mapping, $(A,\eta)$-maximal monotone mapping, generalized resolvent operator

MSC numbers: 49J40, 65B05