Relatively maximal monotone mappings and applications to general inclusions

Abstract

Based on the relative maximal monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems is explored, while generalizing most of the investigations on weak convergence using the proximal point algorithm in a real Hilbert space setting. Furthermore, the main result has been applied to the context of the relative maximal relaxed monotonicity frameworks for solving a general class of variational inclusion problems. It seems that the obtained results can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution inclusions, and the obtained results can further be applied to the Douglas–Rachford splitting method for finding the zero of the sum of two relatively monotone mappings as well.

Keywords:

• inclusion problems
• maximal monotone mapping
• relatively maximal monotone mapping
• generalized resolvent operator

AMS Subject Classifications::

• 49J40
• 47H10
• 65B05