An Elementary Proof of Surjectivity for a Class of Accretive Operators
- 1 July 1979
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 75 (2) , 255-258
- https://doi.org/10.2307/2042752
Abstract
An operator A defined on a real Banach space X is said to be locally accretive if, for each <!-- MATH $\lambda > 0,x \in X$ --> 0,x \in X$"> and each y near x, <!-- MATH $x,\left\| {x - y} \right\| \leqslant \left\| {x - y + \lambda (Ax - Ay)} \right\|$ --> . It is shown that if is locally accretive and locally Lipschitzian then <!-- MATH $(I + A)(X) = X$ --> .
Keywords
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