In a previous paper ([2], see also [4]) we proposed a supervisory control system to globally regulate to zero the state of a very poorly modeled, open-loop unstable but not exponentially unstable, linear process in the presence of input constraints. The process to control was unknown but assumed to belong to a finite family P of nominal models. In this paper, the analysis is extended to the cas...

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

In this paper, a class of generalised best approximation problems is formulated in a fuzzy normed linear space.

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

The claim that follows, which I have called the nite-dimensional normed linear space theorem, essentially says that all such spaces are topologically R with the Euclidean norm. This means that in many cases the intuition we obtain in R,R, and R by imagining intervals, circles, and spheres, respectively, will carry over into not only higher dimension R but also any vector space that has nite dim...

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log dimX = O(log dimV ) and (2) every subspace of X, whose dimension is not “too small,” contains a further wellcomplemented subspace nearly isometric to V . This sheds new light on the structure of ...

Let us consider two nonempty subsets A, B of a normed linear space X , and let us denote by 2B the set of all subsets of B. We introduce a new class of multivalued mappings {T : A → 2B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T (x) : x ∈ A} is nonempty. Using this nonempty intersection theorem, we attempt...