We introduced the notion of (X, dist,V)-boundedness of a filtered family of operators in the Musielak-Orlicz sequence space Xφ of multifunctions. This notion is used to get the convergence theorems for the families of X-linear operators, X-distsublinear operators and X-dist-convex operators. Also, we prove that Xφ is complete.

We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

We study when the existence of an increasing selection can be derived from the monotonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested by A.F. Veinott, Jr. An increasing selection exists if (1) the multifunction is weakly ascending ...

Let F:X-*X be a multifunction on a partially ordered set (X, ¿). Suppose for each pair «iá*2 and for each yi<EF(xi) there is a yi&F{y¿) such that yièyiThen sufficient conditions are given such that multifunctions F satisfying the above condition will have a fixed point. These results generalize the Tarski Theorem on complete lattices, and they also generalize some results of S. Abian and A. B. ...

In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions. 0 Introduction In this paper, we unify three different lines of investigation: the theory of SSD spaces as expounded in [11] and [13], part of the theory of strongly representable multifunctions ...