International Science Index


1483

On the Maximum Theorem: A Constructive Analysis

Abstract:We examine the maximum theorem by Berge from the point of view of Bishop style constructive mathematics. We will show an approximate version of the maximum theorem and the maximum theorem for functions with sequentially locally at most one maximum.
References:
[1] C. Berge. Topological Spaces. Macmillan, 1963.
[2] J. Berger, D. Bridges, and P. Schuster. The fan theorem and unique existence of maxima. Journal of Symbolic Logic, 71:713-720, 2006.
[3] E. Bishop and D. Bridges. Constructive Analysis. Springer, 1985.
[4] K. Border. Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press, 1985.
[5] D. Bridges and F. Richman. Varieties of Constructive Mathematics. Cambridge University Press, 1987.
[6] D. Bridges and L. V╦å─▒t┬©╦ÿa. Techniques of Constructive Mathematics. Springer, 2006.
[7] T. Ichiishi. Game Theory for Economic Analysis. Academic Press, 1983.