this paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous multifunctions and also some characterizations of them are considered.

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 ...

We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunctio...

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 ...

In this survey, we review some old and new results initiated with the study of expansive mappings. From a variational perspective, convergence analysis almost-expansive curves sequences governed by an evolution equation monotone or non-monotone type. Finally, propose two well-defined algorithms to remedy shortcomings concerning ill-posedness expansive-type systems.

The bounded-real and positive-real lemmas solve two important linear-quadratic optimal control problems related to the concepts of non-expansive and passive systems, respectively. The lemmas assume controllability, yet a non-expansive or passive system can be uncontrollable. In this paper, we solve these optimal control problems without assuming controllability. We obtain necessary and sufficie...

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on the Hennessy-Milner logic. The logic for characteris...

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...

an efficient synthesis route to 1,4-dihydropyrimidine derivatives from reaction of divergent aldehydes with ethylacetoacetate and urea under solvent-free conditions by zno nanoparticles as a relative in expansive, eco-friendly, easy available, non-volatile, non-explosion, thermally robust, recyclable and easy to handle catalyst at 90°c with excellent yields is described. unenhanced reaction tim...