대한수학회보 (Bulletin of the Korean Mathematical Society)
- 제26권2호
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- Pages.203-209
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- 1989
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
ON SURJECTIVITY OF m-ACCRETIVE OPERATORS IN BANACH SPACES
- Han, Song-Ho (Kangweon National University) ;
- Kim, Myeong-Hwan (Kangweon National University) ;
- Park, Jong An. (Kangweon National University)
- 발행 : 1989.08.01
초록
Recently many authors [2,3,5,6] proved the existence of zeros of accretive operators and estimated the range of m-accretive operators or compact perturbations of m-accretive operators more sharply. Their results could be obtained from differential equations in Banach spaces or iteration methods or Leray-Schauder degree theory. On the other hand Kirk and Schonberg [9] used the domain invariance theorem of Deimling [3] to prove some general minimum principles for continuous accretive operators. Kirk and Schonberg [10] also obtained the range of m-accretive operators (multi-valued and without any continuity assumption) and the implications of an equivalent boundary conditions. Their fundamental tool of proofs is based on a precise analysis of the orbit of resolvents of m-accretive operator at a specified point in its domain. In this paper we obtain a sufficient condition for m-accretive operators to have a zero. From this we derive Theorem 1 of Kirk and Schonberg [10] and some results of Morales [12, 13] and Torrejon[15]. And we further generalize Theorem 5 of Browder [1] by using Theorem 3 of Kirk and Schonberg [10].
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