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Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps

In: Topics in Fixed Point Theory

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  • Hichem Ben-El-Mechaiekh

    (Brock University, Department of Mathematics)

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.

Suggested Citation

  • Hichem Ben-El-Mechaiekh, 2014. "Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps," Springer Books, in: Saleh Almezel & Qamrul Hasan Ansari & Mohamed Amine Khamsi (ed.), Topics in Fixed Point Theory, edition 127, chapter 0, pages 237-272, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01586-6_7
    DOI: 10.1007/978-3-319-01586-6_7
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