The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone

Details The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone

2010-05-13

arxiv.org/abs/1005.2247v2

Mathematics

Functional Analysis

15 pages Revision

Scientific paper

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $A+B$ provided that $A$ and $B$ are maximal monotone operators such that $\dom A\cap\inte\dom B\neq\varnothing$, $A+N_{\overline{\dom B}}$ is of type (FPV), and $\dom A\cap\overline{\dom B}\subseteq\dom B$. The proof utilizes the Fitzpatrick function in an essential way.

Affiliated with

Also associated with

No associations

Rating

The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-640206