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...

We present some properties regarding diffusion and semi-convexity for fuzzy set multifunctions defined on a ring of subsets of an abstract nonvoid space and taking values in the family of all nonvoid closed subsets of a real normed space. Key–Words: diffused, semi-convex, fuzzy set multifunction, non-atomicity, Darboux property, regular, multimeasure, null-additive.

Our main purpose is to introduce the concepts of upper and lower almost contra- (Λ, sp)-continuous multifunctions. Moreover, several characterizations contra-(Λ, multifunctions are investigated

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

In 1996, Dontchev [14] introduced and investigated a new notion of non-continuity called contra-continuity. Recently, Baker et al. [6] offered a new generalization of contra-continuous functions via λ-closed sets, called almost contra λ-continuous functions. It is the objective of this paper to further study some more properties of such functions.

Recently, Bertsekas and Tsitsiklis proposed a partially asynchronous implementation of the gradient projection algorithm of Goldstein and Levitin and Polyak for the problem of minimizing a differentiable function over a closed convex set. In this paper, we analyze the rate of convergence of this algorithm. We show that if the standard assumptions hold (that is, the solution set is nonempty and ...

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...