Accretive operators which are always single-valued in normed spaces |
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| Institution: | 1. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy;2. Department of Mathematics, University of Alabama in Huntsville, Huntsville, AL 35899, USA;1. Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C6, 1749-016 Lisboa, Portugal;2. The Research Institute of the University of Bucharest (ICUB), University of Bucharest, Bd. M. Kogălniceanu 36-46, 050107, Bucharest, Romania;3. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014, Bucharest, Romania;4. Simion Stoilow Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, 010702 Bucharest, Romania |
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| Abstract: | Set-valued accretive operators in Banach spaces have been extensively studied for several decades. Our main purpose in this paper is to establish a quite revealing result that says that every set-valued lower semi-continuous accretive mapping defined on a normed space is, indeed, single-valued on the interior of its domain. No reference to the well-known Michael’s Selection Theorem is needed. This result is used to extend known theorems concerning the existence of zeros for such operators, as well as showing existence of solutions for variational inclusions. |
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