Title of article :
On sum of range sets of sum of two maximal monotone operators
Author/Authors :
Pradhan, Dillip Kumar Department of Mathematics - National Institute of Technology Rourkela, India , Pattanaik, Suvendu Ranjan Department of Mathematics - National Institute of Technology Rourkela, India
Abstract :
In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish
(1) ran (A+B)=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 Bre´zis-Haraux conditions.
Keywords :
Monotone Operator , Maximal Monotone Operator , Ultramaximal Monotone Operator , Bracuteezis-Haraux conditions
Journal title :
International Journal of Nonlinear Analysis and Applications
