This paper considers non-transferable utility games and provides sufftcient conditions for the existence of the bargaining set introduced in Mas-Cole11 (1989). Our main assumption is weak balancedness. This assumption is weaker than balancedness and is satisfied in all transferable utility games and all three-player games. The proof of our main result is based on an application of a coincidence...

In [2] Fan determines the endomorphism type of a finite projective plane. In this note we show that Fan’s result actually characterizes the class of projective planes among the finite bipartite graphs of diameter three. In fact, this will follow from a generalization of Fan’s theorem and its converse to all finite bipartite graphs with diameter d and girth g such that (1) d + 1 < g ≤ 2d, and (2...

A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results ext...

We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov’s principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak Kön...

Let ‖ · ‖ be a unitary similarity invariant norm on the set Mn of n× n complex matrices. A description is obtained for surjective maps φ on Mn satisfying ‖AB− BA‖ = ‖φ(A)φ(B)−φ(B)φ(A)‖ for all A,B ∈ Mn . The general theorem covers the special cases when the norm is one of the Schatten p -norms, the Ky-Fan k -norms, or the k -numerical radii. Mathematics subject classification (2000): Primary 15...

The concept of convexlike (concavelike) functions was introduced by Ky Fan (1953), who has proved the rst minimax theorem without linear structure of the underlying spaces. Further extensions or generalizations of this concept have been used later in optimization and decision theory, but the most signiicant applications are in the framework of the game theory, where the strategy spaces are not ...

A weighted graph is a graph provided with an edge-weighting function w from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53– 69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to Ore-type one in unweighted graphs, it is shown in [Bondy et al., Discuss....

Recently the author [Proc. Amer. Math. Soc. 103(1988), 11291135] proved random versions of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] for continuous condensing random maps and nonexpansive random maps defined on a closed convex bounded subset in a separable Hilbert space. In this paper, we prove that it is still true for (more general) continuous 1-set-contractiv...

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Zk of order k. We then demonstrate how such a chain map induces a “Zk-combinatorial Stokes theorem”, which in turn implies “Dold’s theorem” that there is no equivariant map from an n-connected to an n-dimensional free Zk-complex. Thus we build a combinatorial access road to probl...