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Similar Journals
 Constructive Mathematical AnalysisNumber of Followers: 1     Open Access journal ISSN (Online) 2651-2939 Published by DergiPark  [100 journals]
• Approximation properties related to the Bell polynomials

• Authors: Mircea IVAN ; Ioan GAVREA
Abstract: The authors provide a complete asymptotic expansion for a class of functions in terms of the completeBell polynomials. In particular, they obtain known asymptotic expansions of some Keller type sequences.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Approximation in weighted spaces of vector functions

• Authors: Gavriil PALTINEANU ; Ileana BUCUR
Abstract: In this paper, we present the duality theory for general weighted space of vector functions. We mention that a characterization of the dual of a weighted space of vector functions in the particular case $V \subset C^{+} (X)$ is mentioned by J. B. Prolla in [6]. Also, we extend de Branges lemma in this new setting for convex cones of a weighted spaces of vector functions (Theorem 4.2). Using this theorem, we find various approximations results for weighted spaces of vector functions: Theorems 4.2-4.6 as well as Corollary 4.3. We mention also that a brief version of this paper, in the particular case $V \subset C^{+} (X)$, is presented in [3], Chapter 2, subparagraph 2.5.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Multivariate sampling Kantorovich operators: quantitative estimates in
Orlicz spaces

• Authors: Laura ANGELONI ; Nursel ÇETİN , Danilo COSTARELLI , Anna Rita SAMBUCINI , Gianluca VINTI
Abstract: In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Durrmeyer type operators on a simplex

Abstract: The paper contains the definition and certain approximation properties of a sequence of Durrmeyer-type operators on a simplex, which preserve affine functions and make a link between the multidimensional "genuine" Durrmeyer operators and the multidimensional Bernstein operators.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Some numerical applications of generalized Bernstein operators

• Authors: Donatella OCCORSIO ; Maria Grazia RUSSO , Woula THEMISTOCLAKIS
Abstract: In this paper some recent applications of the so-called Generalized Bernstein polynomials are collected.This polynomial sequence is constructed by means of the samples of a continuous function f on equispaced points of[0; 1] and depends on an additional parameter which yields the remarkable property of improving the rate of convergenceto the function f, according with the smoothness of f. This means that the sequence does not suffer ofthe saturation phenomena occurring by using the classical Bernstein polynomials or arising in piecewise polynomialapproximation. The applications considered here deal with the numerical integration and the simultaneous approximation.Quadrature rules on equidistant nodes of [0; 1] are studied for the numerical computation of ordinary integralsin one or two dimensions, and usefully employed in Nyström methods for solving Fredholm integral equations. Moreover,the simultaneous approximation of the Hilbert transform and its derivative (the Hadamard transform) is illustrated.For all the applications, some numerical details are given in addition to the error estimates, and the proposedapproximation methods have been implemented providing numerical tests which confirm the theoretical estimates.Some open problems are also introduced.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Unrestricted Cesàro summability of $d$-dimensional Fourier series and
Lebesgue points

• Authors: Ferenc WEİSZ
Abstract: We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Cesàro means of the Fourier series of the multi-dimensional function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge to $f$ at each strong Lebesgue point.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Modulars from Nakano onwards

• Authors: Alberto FIORENZA
Abstract: We discuss and compare a number of notions of modulars appeared in literature, among which there is a selection of the well known ones. We highlight the connections between the various definitions and provide several examples, taken from existing literature, recalling known results and completing the picture with some original considerations
PubDate: Tue, 01 Jun 2021 00:00:00 +030

• Generalized Cesàro summability of Fourier series and its applications

• Authors: Oktay DUMAN
Abstract: In this paper, by using generalized Cesàro means based on q-integers we study on approximating continuous and periodic functions by its Fourier series. We also discuss its connection with the concept of statistical convergence. At the end of the paper, some applications and graphical illustrations are also provided.
PubDate: Tue, 01 Jun 2021 00:00:00 +030

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