Sum of two maximal monotone operators in a general Banach space is maximal

Abstract

In a real Banach space, we first prove that the sum of a monotone operator of type (FPV) and maximal monotone operator Rockafellar's constraint qualification is maximal. This prove leads to the solution of most interesting long-time outstanding problem in monotone operator theory is the sum problem.

The proof in main result is not correct and some assumptions are not true