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