On sum of range sets of sum of two maximal monotone operators

	On sum of range sets of sum of two maximal monotone operators
International Journal of Nonlinear Analysis and Applications
مقاله 75، دوره 12، شماره 1، مرداد 2021، صفحه 927-934 اصل مقاله (399.01 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.12171.1615
نویسندگان
Dillip Kumar Pradhan^* ؛ Suvendu Ranjan Pattanaik
Department of Mathematics, National Institute of Technology, Rourkela, India
چکیده
In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish (1) $\overline{ran (A+B)}=\overline{ran A+ran B}$ (2) int (ran (A+B))=int(ran A+ran B). 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.
کلیدواژه‌ها
Monotone Operator؛ Maximal Monotone Operator؛ Ultramaximal Monotone Operator؛ Br$\acute{e}$zis-Haraux conditions
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