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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: 30 June 2024 | Viewed by 2529

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

Related Special Issue

Published Papers (4 papers)

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Research

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 291
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 481
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 - 05 Jan 2024
Viewed by 851
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 512
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)
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