Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems

Asfaw, Teffera M.

Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems

dc.contributor.author	Asfaw, Teffera M.	en
dc.contributor.department	Mathematics	en
dc.date.accessioned	2017-09-18T09:38:17Z	en
dc.date.available	2017-09-18T09:38:17Z	en
dc.date.issued	2016-08-11	en
dc.date.updated	2017-09-18T09:38:17Z	en
dc.description.abstract	Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let and 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 under weaker sufficient conditions. These theorems improved the well-known maximality results of Rockafellar who used condition and Browder and Hess who used the quasiboundedness of and condition . In particular, the maximality of is proved provided that , where 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.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Teffera 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. doi:10.1155/2016/7826475	en
dc.identifier.doi	https://doi.org/10.1155/2016/7826475	en
dc.identifier.uri	http://hdl.handle.net/10919/78942	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 2016 Teffera M. Asfaw. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems	en
dc.title.serial	Abstract and Applied Analysis	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en