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Axioms
Special Issues
Approximation Theory and Related Applications II
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Approximation Theory and Related Applications II

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 1570

Special Issue Editor

Prof. Dr. Yurii Kharkevych

E-Mail Website
Guest Editor
Department of Theory of Functions and Methods of Teaching Mathematics, Lesya Ukrainka Volyn National University, 13 Voli Ave., 43025 Lutsk, Ukraine
Interests: function theory; approximation theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This issue is a continuation of the previous successful Special Issue “Approximation Theory and Related Applications”.  Thank you for all authors and reviewers. We are glad to announce this Special Issue to collect more works in various aspects of approximation theory.

In this Special Issue, we will cover the field of approximations in special function classes, fractional approximations, approximation operators, approximations of functions of infinitely many variables, numerical analysis, harmonic analysis, spline approximation, stochastic approximation, asymptotic analysis, and applications of approximation theory. Our goal is to gather articles reflecting new trends approximation theory and related topics.

Prof. Dr. Yurii Kharkevych
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

  • approximation operators
  • special functions
  • fractional approximation
  • numerical analysis
  • harmonic analysis
  • functional spaces
  • asymptotic analysis
  • extremal problems
  • approximation of solutions of differential and integral equations
  • approximation in the complex plane
  • interpolation
  • spline approximation
  • stochastic approximation

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Published Papers (1 paper)

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Research

11 pages, 312 KiB  
Article
Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques
by Ramandeep Behl, Himani Arora, Eulalia Martínez and Tajinder Singh
Axioms 2023, 12(3), 270; https://doi.org/10.3390/axioms12030270 - 06 Mar 2023
Viewed by 1016
Abstract
In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non-differentiable. So, we present, [...] Read more.
In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non-differentiable. So, we present, in this paper, iterative methods that do not use the derivative of the non-linear operator in their iterative expression. With our new iterative technique, we find better numerical results of Planck’s radiation, Van Der Waals, Beam designing, and Isothermal continuous stirred tank reactor problems. Divided difference and weight function approaches are adopted for the construction of our schemes. The convergence order is studied thoroughly in the Theorems 1 and 2, for the case when multiplicity p≥2. The obtained numerical results illustrate the preferable outcomes as compared to the existing ones in terms of absolute residual errors, number of iterations, computational order of convergence (COC), and absolute error difference between two consecutive iterations. Full article
(This article belongs to the Special Issue Approximation Theory and Related Applications II)
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