Search results for "Matematica"

Fixed fuzzy points of fuzzy mappings in Hausdorff fuzzy metric spaces with application

2015

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of our results, we investigate the existence of solution for some recurrence relations associated to the analysis of quicksort algorithms.

The completion of a C*-algebra with a locally convex topology

2006

There are examples of C*-algebras A that accept a locally convex *-topology t coarser than the given one, such that Ae[t] (the completion of A with respect to t) is a GB*-algebra. The multiplication of A[t] may be or not be jointly continuous. In the second case, Ae[t] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ae[t] are investigated. If A[t+] denotes the t-closure of the positive cone A+ of the given C*-algebra A, then the property A[t]+ \cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representations of the corresponding *-algebra Ae[t].

Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

2009

Abstract Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.

MR3428804 Reviewed Benci, Vieri(I-PISA); Luperi Baglini, Lorenzo(A-WIENM) Generalized functions beyond distributions. (English, Arabic summary) Arab.…

2016

Generalized functions are here intended to mean a particular class V˜(Ω) of ultrafunctions, i.e. functions defined on a non-Archimedean field that extends a class V(Ω) of L2(Ω)-integrable continuous functions. The particular class of ultrafunctions is selected by some desiderata to obtain the properties sufficient for applications to PDE. One of these is to maintain the locality property of a local operator defined on V(Ω) when it is extended to V˜(Ω). This fact is related to the possibility of defining a sort of orthogonality between "Delta ultrafunctions''. The results are applied to the definition of the derivative operator, the definite integral and to associate an ultrafunction to ever…

On the possible values of upper and lower derivatives with respect to differentiation bases of product structure.

2018

A solution of the Guzmán's problem on possible values of upper and lower derivatives is given for the class of translation invariant and product type differentiation bases formed by ndimensional intervals. Namely, the bases from the mentioned class are characterized, for which integral means of a summable function can boundedly diverge only on a set of zero measure

Dual of the Class of HKr Integrable Functions

2019

We define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space.

A variational henstock integral characterization of the radon-nikodým property

2009

A characterization of Banach spaces possessing the Radon-Nikodym property is given in terms of finitely additive interval functions. We prove that a Banach space X has the RNP if and only if each X-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an X-valued function. Due to that characterization several X-valued set functions that are only finitely additive can be represented as integrals.

Approximation of Banach space valued Riemann type integrable functions by step functions

2008

In this talk we consider the possibility to approximate (with respect to some topology induced by the Alexiewicz norm) non absolutely integrable functions defined on the unit interval by step functions. In particular we show that any Henstock (respectively Henstock-Kurzweil-Pettis, Denjoy-Khintchine-Pettis) integrable functions can be scalarly approximate in the Alexiewicz norm by a sequence of step functions. Moreover the approximation may be done in the Alexiewicz norm if and only if the range of the integral is relatively norm compact (property which is automatically satisfied by the Henstock integrable functions). We also provide an example to show that, unlike the Pettis case, Henstock…

MR3093276 Reviewed Naralenkov, K. M. On continuity and compactness of some vector-valued integrals. Rocky Mountain J. Math. 43 (2013), no. 3, 1015–10…

2014

ZBL MS 63/6 Satco, Bianca-Renata; Turcu, Corneliu-Octavian Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on t…

2013

The authors prove an existence result for a nonlinear integral equation on time scales under weak topology assumption in the target Banach space. In the setting of vector valued functions on time scales they consider the Henstock-Kurzweil-Pettis $\Delta$-integral which is a kind of Henstock integral recently introduced by Cichon, M. [Commun. Math. Anal. 11 (2011), no. 1, 94�110]. In this framework they show the existence of weakly continuous solutions for an integral equation x(t)= f(t, x(t))+ (HKP)\int_0^t g(t,s,x(s)) \Delta s governed by the sum of two operators: a continuous operator and an integral one. The main tool to get the solutions is a generalization of Krasnosel'skii fixed point…