... 150 Fan-Browder fixed point theorem and economic equilibria we show that a number of Urai’s results [12] (e.g., Theorem for the case (K∗ ), Theorem for the case (NK∗ ), Theorem for the case ... equivalent to Theorem 2.1 Proof of Theorem 2.1 using Theorem 2.2 Suppose that there exists M ∈ D such that z∈M F(z) = ∅ under the hypothesis of Theorem 2.1 Let M := {z1 ,z2 , ,zn } and define P:X ... Dekker, New York, 1987, pp 235–244 P W Sy and S Park, The KKM maps and fixed point theorems in convex spaces, Tamkang J Math 34 (2003), no 2, 169–174 K Urai, Fixed point theorems and the existence of...