Maximality Theorems on the Sum of Two Maximal Monotone Operators and Applications to Variational inequality Problems

dc.contributor.authorAsfaw, Teffera M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2016-12-30T13:28:46Zen
dc.date.available2016-12-30T13:28:46Zen
dc.date.issued2016-08-11en
dc.description.abstractLet 𝑋 be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇 : 𝑋 ⊇ 𝐷(𝑇)→ 2𝑋 ∗ and 𝐴 : 𝑋 ⊇ 𝐷(𝐴) → 2𝑋 ∗ be maximal monotone operators.The maximality of the sum of two maximal monotone operators has been an open problem for many years. In this paper, new maximality theorems are proved for 𝑇 + 𝐴 under weaker sufficient conditions. These theorems improved the well-known maximality results of Rockafellar who used condition ∘ 𝐷(𝑇) ∩ 𝐷(𝐴) ≠ 0 and Browder and Hess who used the quasiboundedness of 𝑇 and condition 0 ∈ 𝐷(𝑇) ∩𝐷(𝐴). In particular, the maximality of 𝑇 + 𝜕𝜙 is proved provided that ∘ 𝐷(𝑇) ∩ 𝐷(𝜙) ≠ 0, where 𝜙 : 𝑋 → (−∞,∞] is a proper, convex, and lower semicontinuous function. Consequently, an existence theorem is proved addressing solvability of evolution type variational inequality problem for pseudomonotone perturbation of maximal monotone operator.en
dc.description.notesfalse (Extension publication?)en
dc.description.versionPublished versionen
dc.format.extent1 - 10 (10) page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationTeffera M. Asfaw, "Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems", Abstract and Applied Analysis, vol. 2016, Article ID 7826475, 10 pages, 2016. https://doi.org/10.1155/2016/7826475en
dc.identifier.doihttps://doi.org/10.1155/2016/7826475en
dc.identifier.issn1687-0409en
dc.identifier.urihttp://hdl.handle.net/10919/73910en
dc.identifier.volume2016en
dc.language.isoenen
dc.publisherHindawien
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleMaximality Theorems on the Sum of Two Maximal Monotone Operators and Applications to Variational inequality Problemsen
dc.title.serialAbstract and Applied Analysisen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dcterms.dateAccepted2016-07-17en
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Mathematicsen
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