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Axioms
Special Issues
Advanced Approximation Techniques and Their Applications II
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Advanced Approximation Techniques and Their Applications II

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 27 September 2024 | Viewed by 2461

Special Issue Editor

Prof. Dr. Roman Dmytryshyn

E-Mail Website
Guest Editor
Department of Mathematical and Functional Analysis, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
Interests: approximation theory; continued fractions and their generalizations; special functions; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Approximation theory is one of the most intriguing sections of mathematics, as its application overlaps with both classical and modern analysis, as well as numerical analysis, and even various branches of applied mathematics. Nowadays, due to the development of computer technology and the requirements of natural and engineering sciences, interest in studying various approximation techniques has grown significantly. In the scientific community, this is a continuous stimulus to develop new and better-performing approximation techniques that are able to grasp the particular features of the problem.

The primary purpose of this Special Issue is to highlight the advanced techniques of approximation theory which have a practical application to a wide range of mathematics problems. This, in turn, will enrich mathematical science with profound and fruitful results.

Prof. Dr. Roman Dmytryshyn
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • interpolation in approximation theory
  • approximation by polynomials spline
  • approximation
  • approximation by trigonometric polynomials inequalities in approximation
  • approximation by rational functions
  • Padé approximation
  • rate of convergence
  • inverse theorems in approximation
  • theory simultaneous approximation
  • approximation with constraints
  • approximation by special function classes
  • approximation by operators saturation in approximation theory
  • best constants in approximation theory
  • approximation by arbitrary linear expressions
  • approximation by arbitrary nonlinear expressions
  • uniqueness of best approximation
  • best approximants
  • approximate quadratures
  • numerical approximation
  • series expansions
  • asymptotic approximations
  • asymptotic expansions
  • abstract approximation theory
  • remainders in approximation
  • formulas least-squares
  • methods continued fractions and their generalizations
  • convergence and divergence of infinite limiting processes
  • approximation of solutions of differential equations
  • approximation of solutions of functional-differential equations
  • approximation of solutions of integral equations

Related Special Issue

Published Papers (4 papers)

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Research

21 pages, 331 KiB  
Article
Probabilistic and Average Gel’fand Widths of Sobolev Space Equipped with Gaussian Measure in the Sq-Norm
by Ruihuan Wu, Yuqi Liu and Huan Li
Axioms 2024, 13(7), 492; https://doi.org/10.3390/axioms13070492 - 22 Jul 2024
Viewed by 309
Abstract
In this article, we mainly studied the Gel’fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel’fand (N,δ)-widths of multivariate Sobolev space [...] Read more.
In this article, we mainly studied the Gel’fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel’fand (N,δ)-widths of multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel’fand N-widths of univariate Sobolev space W2r(T) and multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
12 pages, 275 KiB  
Article
Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on ℤp
by Maryam Salem Alatawi, Waseem Ahmad Khan and Ugur Duran
Axioms 2024, 13(7), 421; https://doi.org/10.3390/axioms13070421 - 22 Jun 2024
Viewed by 351
Abstract
Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers [...] Read more.
Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers and polynomials, such as central Fubini, Bernoulli, central Bell, and Changhee numbers and polynomials. One of the key applications of these integrals is for obtaining the symmetric identities of certain special polynomials. In this study, we focus on a novel generalization of degenerate central Fubini polynomials. First, we introduce two variable degenerate w-torsion central Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. Through this representation, we investigate several symmetric identities for these polynomials using special p-adic integral techniques. Also, using series manipulation methods, we obtain an identity of symmetry for the two variable degenerate w-torsion central Fubini polynomials. Finally, we provide a representation of the degenerate differential operator on the two variable degenerate w-torsion central Fubini polynomials related to the degenerate central factorial polynomials of the second kind. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
9 pages, 234 KiB  
Article
Asymptotic Conformality and Polygonal Approximation
by Samuel L. Krushkal
Axioms 2024, 13(6), 376; https://doi.org/10.3390/axioms13060376 - 3 Jun 2024
Viewed by 304
Abstract
Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal [...] Read more.
Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal maps. The paper provides an approximative characterization of local conformality and its connection with univalent polynomials. Also, some other quantitative applications of this connection are given. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
25 pages, 10343 KiB  
Article
Jordan-Type Inequalities and Stratification
by Miloš Mićović and Branko Malešević
Axioms 2024, 13(4), 262; https://doi.org/10.3390/axioms13040262 - 14 Apr 2024
Viewed by 1156
Abstract
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding [...] Read more.
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions. Based on this approach, some optimal approximations of the sinc function are derived by determining the corresponding minimax approximants. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
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