In this paper we examine nonlinear integrodifferential inclusions in R . For the nonconvex problem, we show that the solution set is a retract of the Sobolev space W (T,R ) and the retraction can be chosen to depend continuously on a parameter λ. Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retr...

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...

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.

We prove the existence of viable solutions for an autonomous second-order functional differential inclusions in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the subdifferential of a proper lower semicontinuous convex function.

The existence of monotone solutions for a second-order functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φ-convex function of order two.

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.