 Some Fundamental Topological Fixed Point Theorems for Set-Valued MapsHichem Ben-El-Mechaiekh ()
Chapter Chapter 7 in Topics in Fixed Point Theory, 2014, pp 237-272 from Springer Abstract: Abstract This chapter introduces the reader to two of the most fundamental topological fixed point theorems for set-valued maps: the Browder–Ky Fan and the Kakutani–Ky Fan theorems. It provides a concise discussion including motivations, techniques, as well as some most important applications. The exposition is driven by clarity and simplicity. Generality of statements is deliberately sacrificed to the benefit of conceptual significance. Generalizations based on technicalities or artificial definitions which, with little effort, can be reduced to classical settings are set aside, unless they are motivated by convincing applications. Rather, the treatment here is reduced to the classical convex case, which is—we firmly believe—where the essence belongs. The arguments are kept elementary, as to allow the use of this chapter in a first course in topological fixed point theory and its applications. Keywords: Topological Space; Fixed Point Theorem; Topological Vector Space; Continuous Selection; Coincidence Theorem (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01586-6_7 Ordering information: This item can be ordered from DOI: 10.1007/978-3-319-01586-6_7 Access Statistics for this chapter More chapters in Springer Books from Springer |
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