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The most important open problem in Monotone Operator Theory concerns themaximal monotonicity of the sum of two maximally monotone operators providedthat the classical Rockafellar's constraint qualification holds.  In this paper, we establish the maximal monotonicity of $A+B$ provided that$A$ and $B$ are maximally monotone operators such that $\sta(\domA)\cap\inte\dom B\neq\varnothing$, and $A$ is of type (FPV). We show that whenalso $\dom A$ is convex, the sum operator: $A+B$ is also of type (FPV). Ourresult generalizes and unifies several recent sum theorems.

Sum theorems for maximally monotone operators of type (FPV)