Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.

Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K , with the sup-norm. Types over C(K) (in the sense of Krivine and Maurey) can be uniquely represented by pairs ( ,u) of bounded real-valued functions on K , where is lower semicontinuous, u is upper semicontinuous, ≤ u, and (x) = u(x) for all isolated points x of K . A condition that charac...

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...

We study whether we can weaken the conditions given in Reny [4] and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy ε−equilibria for all ε > 0. We show by examples that there are: 1. quasiconcave, payoff secure games without pure strategy ε−equilibria for small enough ε > 0 (and hence, without pure strategy Nash...

In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t?1)) along with a certain family of time discretizations with stepsize 1=n. In the original problem, the attractor admits a Morse decomposition. We proved in G,H] that the discretized problems have global attractors. It was proved in G,M] that such attractors also admit Morse decompositions. In G,H] w...

Let X be a convex subset of a locally convex topological vector space, let U ⊂ X be open with U compact, let F : U → X be an upper semicontinuous convex valued correspondence with no fixed points in U \U , let P be a compact absolute neighborhood retract, and let ρ : U → P be a continuous function. We show that if the fixed point index of F is not zero, then there is a neighborhood V of F in th...

The paper studies the solution stability of a parametric control problem governed by semilinear elliptic equations with mixed state-control constraint, where objective function is nonconvex and admissible set unbounded. We show that under certain conditions, upper semicontinuous continuous respect to parameters.

Let σ be a positive number and Cσ := C([−σ, 0], R) the Banach space of continuous functions from [−σ, 0] into R and let T (t) be the operator from C([−σ, T ], R) into Cσ, defined by (T (t)x)(s) := x(t + s), s ∈ [−σ, 0]. We prove the existence of solutions for functional differential inclusion(differential inclusions with memory) x′ ∈ F (T (t)x) + f(t, T (t)x) where F is upper semicontinuous, co...