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I am looking for encyclopedic references for fixed point theory and its applications. What is the best reference for this subject? thank you.

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Fixed-point theorems for compact convex sets by Mahlon M day has its introductory remarks regarding the history of Fixed-point theorems.

A Fixed Point Theorem for Mappings which do not Increase Distances by W. A. Kirk (Source: The American Mathematical Monthly)

A Generalisation of Brouwer's Fixed Point Theorem by Shizuo Kakutani

Some Properties of Convex Sets Related to Fixed Point Theorems by Ky Fan (Source: Mathematische Annalen)

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  • W.A. Kirk, "History and methods of metric fixed point theory", in Antipodal Points and Fixed Points, 1995.

  • Handbook of Metric Fixed Point Theory, edited by Kirk and Sims, 2001.

  • Handbook of Topological Fixed Point Theory, edited by Brown et al., 2005.

  • History of Algebraic and Differential Topology, by Dieudonné.

  • History of Topology, edited by James, 1999.

  • S. Park, "Ninety Years of the Brouwer Fixed Point Theorem", Vietnam Journal of Mathematics Volume 27, Number 3, 1999.

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