Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212120210501On sum of range sets of sum of two maximal monotone operators927934494710.22075/ijnaa.2019.12171.1615ENDillip KumarPradhanDepartment of Mathematics,
National Institute of Technology, Rourkela, IndiaSuvendu RanjanPattanaikDepartment of Mathematics, National Institute of Technology, Rourkela, IndiaJournal Article20170805In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish <br />(1) $\overline{ran (A+B)}=\overline{ran A+ran B}$<br />(2) int (ran (A+B))=int(ran A+ran B).<br />with the assumption that A is a maximal monotone operator and B is a single-valued maximal monotone operator such that A+B is ultramaximally monotone. Conditions (1) and (2) are known as Br$\acute{e}$zis-Haraux conditions.https://ijnaa.semnan.ac.ir/article_4947_b975f080c7f786e01df5b1594445f48c.pdf