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Zbl 0542.47042
Morales, Claudio
Nonlinear equations involving m-accretive operators. (English)
[J] J. Math. Anal. Appl. 97, 329-336 (1983). ISSN 0022-247X

This paper mainly deals with multivalued, m-accretive operators T in Banach spaces X, having the fixed point property for nonexpansive self- mappings on nonempty, bounded, closed, convex subsets. Besides, the following two results are derived: \par (1) $0\in ran(T),$ iff $\{x\in dom(T)\vert \exists t<0:tx\in Tx\}$ is bounded, or iff there exists some $x\sb 0\in dom(T)$ and an open, bounded neighborhood U of $x\sb 0$ such that $t(x-x\sb 0)\not\in Tx$ for all $x\in \partial U\cap dom(T)$ and $t<0.$ \par (2) The open ball $B(0,r)$ is contained in $ran(T),$ if there exists some $x\sb 0\in dom(T)$ and some U like above with $\Vert T(x\sb 0)\Vert<r\le \Vert T(x)\Vert$ for all $x\in dom(T)\cap \partial U.$ The latter extends a result of {\it A. G. Kartsatos} [J. Math. Anal. Appl. 82, 169-183 (1981; Zbl 0466.47035)].
[G.Hetzer]

MSC 2000:: *47H06 Accretive operators, etc. (nonlinear)

Keywords: multivalued, m-accretive operators; fixed point property for nonexpansive self-mappings on nonempty, bounded, closed, convex subsets

Citations: Zbl 0466.47035

Cited in: Zbl 0824.47053

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