Maximality of the sum of the subdifferential operator and a maximally monotone operator
نویسنده
چکیده
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds, which is called the “sum problem”. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that domA ∩ int domB 6= ∅, and A + N domA is of type (FPV). This generalizes various current results and also gives an affirmative answer to a problem posed by Borwein and Yao. Moreover, we present an equivalent description of the sum problem. 2010 Mathematics Subject Classification: Primary 47H05; Secondary 49N15, 52A41, 90C25
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The sum of two maximal monotone operator is of type FPV
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