In this paper a new type of fuzzy multifunction termed as δ-precontinuous fuzzy multifunction has been introduced and studied. Some characterizations and several properties of this multifunction are obtained. We also characterize this multifunction by newly define fuzzy neighbourhood of a fuzzy set in a fuzzy topological space. Finally, in the last section some applications of this fuzzy multif...

Let F = F(t, x) be a bounded, Hausdorff continuous multifunction with compact, totally disconnected values. Given any y0 ∈ F(t0, x0), we show that the differential inclusion ẋ ∈ F(t, x)⊂ Rm has a globally defined classical solution, with x(t0)= x0, ẋ(t0)= y0. © 2008 Elsevier Inc. All rights reserved.

In this paper we consider nonconvex evolution inclusions driven by time dependent convex subdifferentials. First we establish the existence of a continuous selection for the solution multifunction and then we use that selection to show that the solution set is path connected. Two examples are also presented.

Solutions of the Hamilton-Jacobi equation H(x,−Du(x)) = 1, with H(·, p) Hölder continuous and H(x, ·) convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the C-regularity of the extremal trajectories associated with the multifunction generated by DpH .

The objective of this paper is to obtain the properties of αψcompact spaces by using nets, filterbase, αψ-complete accumulation points and so on. We also investigate some properties of αψ-continuous multifunctions and αψ-compact spaces in the context of multifunction.

Let F be a multifunction from a metric space X into L, and B a subset of X . We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F (x) for x ∈ B.

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex ...

Let mIO(X) be the family of ⋆-open (resp. α-I-open, pre-I-open, semi-I-open, β-I-open, etc.) sets in an ideal topological space (X, τ, I). By using mIO(X), we introduce and investigate notions m-I-continuous multifunction F : I) → (Y, σ) mi⋆ -continuous σ, J). The notion -continuity is a generalization m-I-continuity i⋆-continuity [9].

Relying on the continuous approximate selection method of Cellina, ideas and techniques from Sobolev spaces can be applied to the theory of multifunctions and differential inclusions. The first part of this paper introduces a concept of graph completion, which extends the earlier construction in [10] to functions of several space variables. The second part introduces the notion of Cellina W 1,p...

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description ...