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J. Korean Math. Soc. 2011; 48(3): 641-653
Printed May 1, 2011
https://doi.org/10.4134/JKMS.2011.48.3.641
Copyright © The Korean Mathematical Society.
Multivalued versions of a Bolzano's theorem
Jong-Sook Bae and Seong-Hoon Cho
Moyngji University, Hanseo University
The intermediate value theorem for a continuous real valued function is a kind of Bolzano's theorem. Similar results also hold for compact, monotone or accretive mappings in Banach spaces. In this paper we give multivalued versions of Bolzano's theorem.
Keywords: fixed point, weakly inward set, monotone mapping, semi-monotone mapping, strongly-monotone mapping
MSC numbers: 47H10, 54H25
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