Modern Problems of Analysis, Optimization, Approximation and Their Applications

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

Deadline for manuscript submissions: 30 June 2026 | Viewed by 1149

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Department of Mathematical and Functional Analysis, Vasyl Stefanyk Carpathian National University, 57 Shevchenko str., 76018 Ivano-Frankivsk, Ukraine
Interests: approximation theory; continued fractions and their generalizations; special functions; numerical analysis
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Dear Colleagues,

Today, researchers face well-known, new, simple, and complex problems in all fields of science and technology. Special issues of scientific journals, monographs, social networks, and various thematic forums are platforms where the efforts to solve these problems are concentrated.

The purpose of this Special Issue is to highlight modern results in the fields of linear and nonlinear functional analysis, function theory, approximation theory, numerical analysis, optimization theory, the theory of differential equations, and various applications to real-world problems.

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Prof. Dr. Roman Dmytryshyn
Guest Editor

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Keywords

  • approximations and expansions
  • calculus of variations and optimal control
  • continued fractions and their generalizations
  • difference and functional equations
  • functional analysis
  • functions in complex variables
  • integral equations
  • integral equations
  • number theory
  • numerical analysis
  • operator theory
  • ordinary differential equations
  • partial differential equations
  • real functions
  • sequences, series, and summability
  • several complex variables and analytic spaces
  • special functions

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Published Papers (3 papers)

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Research

14 pages, 278 KB  
Article
On the Domain of Analytical Continuation of the Ratios of Generalized Hypergeometric Functions 3F2
by Roman Dmytryshyn, Marta Dmytryshyn and Sofiia Hladun
Axioms 2025, 14(12), 871; https://doi.org/10.3390/axioms14120871 (registering DOI) - 27 Nov 2025
Viewed by 88
Abstract
The paper considers the problem of the analytical extension of the ratios of generalized hypergeometric functions F23 A new domain of analytic continuation for these ratios under certain conditions to parameters is established. In this case, the domain of analytic extension [...] Read more.
The paper considers the problem of the analytical extension of the ratios of generalized hypergeometric functions F23 A new domain of analytic continuation for these ratios under certain conditions to parameters is established. In this case, the domain of analytic extension of the special function is the domain of convergence of its branched continued fraction expansion. This paper also provides an example of applying the obtained results to dilogarithm function. Full article
15 pages, 268 KB  
Article
Algorithms for Solving the Resolvent of the Sum of Two Maximal Monotone Operators with a Finite Family of Nonexpansive Operators
by Ali Berrailes and Abdallah Beddani
Axioms 2025, 14(11), 783; https://doi.org/10.3390/axioms14110783 - 25 Oct 2025
Viewed by 256
Abstract
In this paper, we address a variational problem involving the sum of two maximal monotone operators combined with a finite family of nonexpansive operators. To solve this problem, we propose iterative algorithms based on single-valued mappings. First, we examine cases involving two or [...] Read more.
In this paper, we address a variational problem involving the sum of two maximal monotone operators combined with a finite family of nonexpansive operators. To solve this problem, we propose iterative algorithms based on single-valued mappings. First, we examine cases involving two or three maximal monotone operators, introducing novel algorithms to obtain their solutions. Secondly, we extend our analysis by applying the Ishikawa iterative scheme within the framework of fixed-point theory. This allows us to establish strong convergence results. Finally, we provide an illustrative example to demonstrate the effectiveness and applicability of the proposed methods. Full article
16 pages, 298 KB  
Article
Interior Approximate Controllability of a Class of Nonlinear Thermoelastic Plate Equations
by Cosme Duque, Hugo Leiva and Zoraida Sivoli
Axioms 2025, 14(9), 682; https://doi.org/10.3390/axioms14090682 - 4 Sep 2025
Viewed by 473
Abstract
This article introduces new sufficient conditions ensuring the interior approximate controllability of semilinear thermoelastic plate equations subject to Dirichlet boundary conditions. The analysis is carried out by reformulating the system as an abstract evolution equation on a suitable Banach space. A key role [...] Read more.
This article introduces new sufficient conditions ensuring the interior approximate controllability of semilinear thermoelastic plate equations subject to Dirichlet boundary conditions. The analysis is carried out by reformulating the system as an abstract evolution equation on a suitable Banach space. A key role is played by the compactness of the semigroup generated by the linear operator, which allows us to treat the nonlinear components effectively. To establish controllability, we apply Rothe’s fixed-point theorem, which provides the necessary framework for handling nonlinear perturbations. The results obtained contribute to the existing literature, since the controllability of the specific semilinear thermoelastic system considered here has not been previously investigated. Full article
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