An Additive Subfamily of Enlargements of a Maximally Monotone Operator
نویسندگان
چکیده
منابع مشابه
Monotone Operators without Enlargements
Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable operators in reflexive Banach spaces and has also given some partial results in the nonreflexive case. In the present paper, we provide another characterization...
متن کاملMaximality of the sum of the subdifferential operator and a maximally monotone operator
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= ∅,...
متن کاملMaximality of the sum of a maximally monotone linear relation and a maximally monotone operator Dedicated to Petar Kenderov on the occasion of his seventieth birthday
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar’s constraint qualification holds. In this paper, we prove the maximal monotonicity of A+B provided that A,B are maximally monotone and A is a linear relation, as soon as Rockafellar’s constraint qualification holds: domA ∩ int domB 6...
متن کاملSome results on the convexity of the closure of the domain of a maximally monotone operator
We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons. 2010 Mathematics Subject Classification: Primary 47H05; Secondary 26B25,47A05, 47B65.
متن کاملEvery maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type
We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide. 2010 Mathematics Subject Classification: Primary 47H05; Secondary 46B10, 47N10, 90C25
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Set-Valued and Variational Analysis
سال: 2015
ISSN: 1877-0533,1877-0541
DOI: 10.1007/s11228-015-0340-9