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Axioms
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Theory of Functions and Applications II
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Theory of Functions and Applications II

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

Deadline for manuscript submissions: 20 January 2025 | Viewed by 6258

Special Issue Editor

Dr. Inna Kalchuk

E-Mail Website
Guest Editor
Faculty of Information Technologies and Mathematics, Lesya Ukrainka Volyn National University, 43025 Lutsk, Ukraine
Interests: approximation theory; theory of function; asymptotic methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue entitled, "Theory of Functions and Applications". This Special Issue aims to publish new and modern results in the field of the theory of functions, and in particular, those related to the theory of functions of a real variable, the theory of approximations, the theory of functions of a complex variable, and the theory of entire and meromorphic functions. The applied aspects of the theory of functions are also of particular interest.

We invite both specialists of function theory and specialists in the related fields of mathematics to publish the results of their research in this Special Issue. We welcome both original and review research articles concerning the latest research on function theory, as well as its applications.

We look forward to receiving your submissions of innovative research that will significantly contribute to the scientific and mathematical community.

Dr. Inna Kalchuk
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

  • theory of functions of a real variable
  • approximation theory
  • asymptotic analysis
  • approximation of solutions of differential and integral equations
  • trigonometric polynomials, inequalities, and extremal problems
  • harmonic analysis
  • theory of functions of complex variables
  • analytic functions and their generalizations
  • entire and meromorphic functions
  • applications involving function theory of real and complex analyses

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Further information on MDPI's Special Issue polices can be found here.

Related Special Issue

Published Papers (8 papers)

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Research

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14 pages, 257 KiB  
Article
Necessary and Sufficient Conditions for the Boundedness of Multiple Integral Operators with Super-Homogeneous Kernels in Weighted Lebesgue Space
by Yong Hong, Bing He and Lijuan Zhang
Axioms 2024, 13(11), 742; https://doi.org/10.3390/axioms13110742 - 29 Oct 2024
Viewed by 190
Abstract
Super-homogeneous functions including homogeneous functions, quasi-homogeneous functions, and several non-homogeneous functions are considered. Using the weight function method, the construction conditions of Hilbert-type multiple integral inequalities with super-homogeneous kernels are first discussed. Then, using the obtained results, the construction problem of bounded multiple [...] Read more.
Super-homogeneous functions including homogeneous functions, quasi-homogeneous functions, and several non-homogeneous functions are considered. Using the weight function method, the construction conditions of Hilbert-type multiple integral inequalities with super-homogeneous kernels are first discussed. Then, using the obtained results, the construction problem of bounded multiple integral operators with super-homogeneous kernels in weighted Lebesgue space is discussed, and the necessary and sufficient conditions for operator boundedness and the operator norm formula are obtained. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
11 pages, 614 KiB  
Article
Necessary and Sufficient Criteria for a Four-Weight Weak-Type Maximal Inequality in the Orlicz Class
by Erxin Zhang
Axioms 2024, 13(9), 635; https://doi.org/10.3390/axioms13090635 - 17 Sep 2024
Viewed by 496
Abstract
Let Φi(i=1,2) be two N-functions, f be a μ-measurable function, and ωi(i=1,2,3,4) be four weight functions. This study presents necessary and [...] Read more.
Let Φi(i=1,2) be two N-functions, f be a μ-measurable function, and ωi(i=1,2,3,4) be four weight functions. This study presents necessary and sufficient conditions for weight functions (ω1,ω2,ω3,ω4) such that the inequality ∫{x:Mf(x)>λ}Φ1(λω1(x))ω2(x)dμ(x)≤c1∫XΦ2(c1|f(x)|ω3(x))ω4(x)dμ(x) holds, which extends several established results. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
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11 pages, 299 KiB  
Article
Concerning Transformations of Bases Associated with Unimodular diag(1, −1, −1)-Matrices
by I. A. Shilin and Junesang Choi
Axioms 2024, 13(7), 452; https://doi.org/10.3390/axioms13070452 - 4 Jul 2024
Cited by 1 | Viewed by 500
Abstract
Considering a representation space for a group of unimodular diag(1, −1, −1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some [...] Read more.
Considering a representation space for a group of unimodular diag(1, −1, −1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some one-parameter subgroups. Finding the kernels of base transformation integral operators in terms of special functions, we consider the compositions of some of these transformations. Since composition is a ‘closed’ operation on the set of base transformations, we obtain some integral relations for the special functions involved in the above kernels. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
12 pages, 279 KiB  
Article
A Unified Representation of q- and h-Integrals and Consequences in Inequalities
by Da Shi, Ghulam Farid, Bakri Adam Ibrahim Younis, Hanaa Abu-Zinadah and Matloob Anwar
Axioms 2024, 13(4), 278; https://doi.org/10.3390/axioms13040278 - 22 Apr 2024
Viewed by 917
Abstract
This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called q−h-derivative/q−h-integral. These notions are further extended on the finite interval [a,b] in the [...] Read more.
This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called q−h-derivative/q−h-integral. These notions are further extended on the finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities for q−h-integrals are studied and directly connected with well known results in diverse fields of science and engineering. The theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified using the q−h-derivative/q−h-integral concept. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
15 pages, 276 KiB  
Article
Exploring Explicit Definite Integral Formulae with Trigonometric and Hyperbolic Functions
by Yulei Chen and Dongwei Guo
Axioms 2024, 13(4), 230; https://doi.org/10.3390/axioms13040230 - 31 Mar 2024
Viewed by 879
Abstract
Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan’s constant, Dirichlet’s beta function, and Riemann’s zeta function, as well as π [...] Read more.
Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan’s constant, Dirichlet’s beta function, and Riemann’s zeta function, as well as π in the denominator. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
19 pages, 424 KiB  
Article
On Construction of Bounded Sets Not Admitting a General Type of Riesz Spectrum
by Dae Gwan Lee
Axioms 2024, 13(1), 36; https://doi.org/10.3390/axioms13010036 - 5 Jan 2024
Cited by 2 | Viewed by 1131
Abstract
We construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant. As a consequence, we obtain a bounded set V with an arbitrarily small Lebesgue [...] Read more.
We construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant. As a consequence, we obtain a bounded set V with an arbitrarily small Lebesgue measure such that for any positive integer N, the set of exponentials with frequencies in any union of cosets of NZ cannot be a frame for the space of square integrable functions over V. These results are based on the proof technique of Olevskii and Ulanovskii from 2008. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
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15 pages, 293 KiB  
Article
A Note on the New Ostrowski and Hadamard Type Inequalities via the Hölder–İşcan Inequality
by Çetin Yildiz, Juan E. Nápoles Valdés and Luminiţa-Ioana Cotîrlă
Axioms 2023, 12(10), 931; https://doi.org/10.3390/axioms12100931 - 28 Sep 2023
Cited by 1 | Viewed by 723
Abstract
For all convex functions, the Hermite–Hadamard inequality is already well known in convex analysis. In this regard, Hermite–Hadamard and Ostrowski type inequalities were obtained using exponential type convex functions in this work. In addition, new generalizations were found for different values of θ [...] Read more.
For all convex functions, the Hermite–Hadamard inequality is already well known in convex analysis. In this regard, Hermite–Hadamard and Ostrowski type inequalities were obtained using exponential type convex functions in this work. In addition, new generalizations were found for different values of θ. In conclusion, we believe that our work’s technique will inspire more study in this field. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)

Review

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55 pages, 1974 KiB  
Review
Exploring the Landscape of Fractional-Order Models in Epidemiology: A Comparative Simulation Study
by Ritu Agarwal, Pooja Airan and Ravi P. Agarwal
Axioms 2024, 13(8), 545; https://doi.org/10.3390/axioms13080545 - 11 Aug 2024
Viewed by 720
Abstract
Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including [...] Read more.
Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
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