Fixed Point and Equilibrium

Hoang Tuy
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Hoang Tuy: Institute of Mathematics

Chapter Chapter 3 in Convex Analysis and Global Optimization, 2016, pp 87-102 from Springer

Abstract: Abstract This chapter summarizes the modern theory of fixed point and equilibrium. Based on the concept of ɛ-approximate minimum, Ekeland variational principle is established first, along with Caristi fixed point theorem, and Nadler contraction theorem for set-valued maps. The next central result is a general equilibrium theorem from which virtually all important fixed point and equilibrium propositions can be derived in a simple unified manner: Ky Fan inequality, Brouwer and Kakutani fixed point theorems, Nash equilibrium theorem, and also the basic solvability theorem for variational inequalities.

Keywords: Nash Equilibrium; Variational Inequality; Fixed Point Theorem; Minimax Theorem; Ekeland Variational Principle (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-31484-6_3

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