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 1376

Special Issue Editor


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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
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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

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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

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Published Papers (2 papers)

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Research

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 150
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 977
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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