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Fixed Point and Equilibrium

In: Convex Analysis and Global Optimization

Author

Listed:
  • Hoang Tuy

    (Institute of Mathematics)

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.

Suggested Citation

  • Hoang Tuy, 2016. "Fixed Point and Equilibrium," Springer Optimization and Its Applications, in: Convex Analysis and Global Optimization, edition 2, chapter 0, pages 87-102, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31484-6_3
    DOI: 10.1007/978-3-319-31484-6_3
    as

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