Equilibrium value and measure of systems of functions | Zendy

Yi-Ju Chao | Zendy; Fon-Che Liu | Zendy

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Equilibrium value and measure of systems of functions

Author(s) -

Yi-Ju Chao,

Fon-Che Liu

Publication year - 1995

Publication title -

topological methods in nonlinear analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.623

H-Index - 23

ISSN - 1230-3429

DOI - 10.12775/tmna.1995.016

Subject(s) - mathematics , measure (data warehouse) , value (mathematics) , mathematical economics , statistics , computer science , data mining

If λ and μ satisfy (1), then λ is called an equilibrium value and μ an equilibrium measure of the systems {fi}, {gi} in this order. If μ is supported by a point x0, then x0 is called an equilibrium point of the systems {fi}, {gi}. Let S be the standard (n − 1)-simplex in R, i.e. S is the set of all those points x = (x1, . . . , xn) of R with all xi ≥ 0 and ∑n i=1 xi = 1. In [3] Ky Fan has shown the existence and uniqueness of an equilibrium value and an equilibrium point of systems {f1, . . . , fn}, {g1, . . . , gn} of continuous functions defined on S under the following conditions:

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