Abstract.A new application-oriented notion of relative maximal monotonicity is introduced and then it is applied to the approximation solvability of a general class of inclusion problems, while generalizing Rockafellar's Theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting. Linear convergence analysis, based on the new model, seems to be simple and compact, and can be applied to generalizing the Yosida approximation and its further applications to first-order evolution equations as well as evolution inclusions.

Received: October 25, 2009

AMS Subject Classification: 49J40, 47H10, 65B05

Key Words and Phrases: inclusion problems, maximal monotone mapping, relative maximal monotone mapping, generalized resolvent operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 2