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The multiple sets split system of mixed type equilibrium problems (MSSMVIP-5) is defined as follows.
The split mixed type equilibrium problem (MSSMVIP-6) is defined as follows.
It represents optimal preferences in some Arrow-Debreu type models or Nash type equilibrium points for some abstract noncooperative games, see, for example, [6] and [7].
The classical continuum mechanical model of granular media of rational thermodynamics results in a Coulomb Mohr type equilibrium stress strain relation.
Complete analytical solutions are given in the optimal situation, for the case of mass-action law equilibria with unity exponents (Langmuir type equilibrium).
(VI) In 2002, Lin and Cheng [21] applied Proposition 5.1 to the existence results of two types of equilibrium problems--the constrained or the competitive Nash type equilibrium problems with multivalued payoff functions.
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Hyperbolic-type equilibrium requires that all the real parts of the corresponding eigenvalues are nonzero.
From Theorem 8.1, we obtain the following form of the Nash-Fan-type equilibrium theorems in [27] with different proofs.
From Theorem 9.1 for, we obtain the following form of the Nash-Fan-type equilibrium theorem for abstract convex spaces.
They added that -spaces satisfy the properties of the Fan type minimax inequality, Fan-Browder-type fixed point, and the Nash-type equilibrium.
The following examples are generalized forms of quasi equilibrium theorem or social equilibrium existence theorems which directly imply generalizations of the Nash-Ma-type equilibrium existence theorem.
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