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Axioms
Special Issues
Recent Advances in Complex Analysis and Related Topics
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Recent Advances in Complex Analysis and Related Topics

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3010

Special Issue Editor

Prof. Dr. Andriy Bandura

E-Mail Website
Guest Editor
Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 76019 Ivano-Frankivsk, Ukraine
Interests: entire function; meromorphic function; analytic function; growth estimates; bounded index; bounded index in a direction; bounded index in joint variables; slice holomorphic function; unit ball; polydisc; vector-valued analytic function; unit disc; Reinhardt domain; value distribution; Fueter regular function; regular quaternionic function
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We have the intention of launching this Special Issue of Axioms. The central topic in this Special Issue will be complex analysis and its applications. We aim to give an opportunity to showcase recent contributions in the many branches of both theoretical and practical studies in complex analysis and its extensions and generalizations. Modern complex analysis is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics, approximation theory, ordinary and partial differential equations, and their systems. Complex analysis also has many applications in engineering fields and physics.

Among the topics that this Special Issue will address, we may consider the following non-exhaustive list: analytic functions; applications of complex analysis; the analytic theory of differential equations; the geometric function theory; Dirichlet series; and meromorphic functions.

The Special Issue is open to receiving further related topics of complex analysis.

In the hopes that this initiative is of interest, we encourage you to submit your current original research paper to be included in this Special Issue.

This Special Issue is a continuation of two previous successful Special Issues:

(1) Honorary Special Issue dedicated to Prof. Anatolii Asirovich Gol’dberg (1930–2008)
https://www.mdpi.com/journal/axioms/special_issues/8YL0K99FO3

(2) Complex analysis
https://www.mdpi.com/journal/axioms/special_issues/complex_analysis

Prof. Dr. Andriy Bandura
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

  • entire functions of several variables
  • analytic functions of several variables
  • growth estimates
  • applications of complex analysis
  • unit ball
  • unit polydisc
  • Reinhardt domain
  • geometric function theory
  • meromorphic functions
  • regular functions
  • Nevanlinna theory
  • Dirichlet series
  • slice holomorphic functions
  • entire curves
  • vector-valued entire functions

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

Related Special Issues

Published Papers (5 papers)

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Research

17 pages, 292 KiB  
Article
Arbitrary Random Variables and Wiman’s Inequality
by Andriy Kuryliak, Oleh Skaskiv and Andriy Bandura
Axioms 2024, 13(11), 739; https://doi.org/10.3390/axioms13110739 - 29 Oct 2024
Viewed by 463
Abstract
We study the class of random entire functions given by power series, in which the coefficients are formed as the product of an arbitrary sequence of complex numbers and two sequences of random variables. One of them is the Rademacher sequence, and the [...] Read more.
We study the class of random entire functions given by power series, in which the coefficients are formed as the product of an arbitrary sequence of complex numbers and two sequences of random variables. One of them is the Rademacher sequence, and the other is an arbitrary complex-valued sequence from the class of sequences of random variables, determined by a certain restriction on the growth of absolute moments of a fixed degree from the maximum of the module of each finite subset of random variables. In the paper we prove sharp Wiman–Valiron’s type inequality for such random entire functions, which for given p∈(0;1) holds with a probability p outside some set of finite logarithmic measure. We also considered another class of random entire functions given by power series with coefficients, which, as above, are pairwise products of the elements of an arbitrary sequence of complex numbers and a sequence of complex-valued random variables described above. In this case, similar new statements about not improvable inequalities are also obtained. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
9 pages, 227 KiB  
Article
A Variational Theory for Biunivalent Holomorphic Functions
by Samuel L. Krushkal
Axioms 2024, 13(9), 628; https://doi.org/10.3390/axioms13090628 - 13 Sep 2024
Viewed by 401
Abstract
Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. This class has been investigated by many authors, mainly to find the coefficient estimates. The assumption of biunivalence is rigid; [...] Read more.
Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. This class has been investigated by many authors, mainly to find the coefficient estimates. The assumption of biunivalence is rigid; this rigidity means that, for example, only the initial Taylor coefficients have been estimated. The aim of this paper is to develop a variational technique for biunivalent functions, which provides a power tool for solving the general extremal problems on the classes of such functions. It involves quasiconformal analysis. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
24 pages, 362 KiB  
Article
Boundedness and Compactness of Weighted Composition Operators from (α, k)-Bloch Spaces to A(β,k) Spaces on Generalized Hua Domains of the Fourth Kind
by Jiaqi Wang and Jianbing Su
Axioms 2024, 13(8), 539; https://doi.org/10.3390/axioms13080539 - 8 Aug 2024
Cited by 1 | Viewed by 505
Abstract
This paper addresses the weighted composition operators Cϕψ from the (α,k)-Bloch spaces to the A(β,k) spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the [...] Read more.
This paper addresses the weighted composition operators Cϕψ from the (α,k)-Bloch spaces to the A(β,k) spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the fourth kind. Additionally, we obtain some necessary and sufficient conditions for the boundedness and compactness of these operators. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
16 pages, 307 KiB  
Article
On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series
by Myroslav Sheremeta and Oksana Mulyava
Axioms 2024, 13(7), 487; https://doi.org/10.3390/axioms13070487 - 19 Jul 2024
Viewed by 473
Abstract
For the Dirichlet series F(s)=∑n=1∞fnexp{sλn}, which is the Hadamard composition of the genus m of similar Dirichlet series Fj(s) with the [...] Read more.
For the Dirichlet series F(s)=∑n=1∞fnexp{sλn}, which is the Hadamard composition of the genus m of similar Dirichlet series Fj(s) with the same exponents, the growth with respect to the function G(s) given as the Dirichlet series is studied in terms of the Φ-type (the upper limit of MG−1(MF(σ))/Φ(σ) as σ↑A) and convergence Φ-class defined by the condition ∫σ0AΦ′(σ)MG−1(MF(σ))Φ2(σ)dσ<+∞, where MF(σ) is the maximum modulus of the function F at an imaginary line and A is the abscissa of the absolute convergence. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
23 pages, 360 KiB  
Article
Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function
by Rashid Ali, Mohsan Raza and Teodor Bulboacă
Axioms 2024, 13(7), 442; https://doi.org/10.3390/axioms13070442 - 29 Jun 2024
Viewed by 725
Abstract
Let Scos* denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf′(z)f(z)≺cosz. In the first result of this article, we [...] Read more.
Let Scos* denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf′(z)f(z)≺cosz. In the first result of this article, we find the sharp upper bounds for the initial coefficients a3, a4 and a5 and the sharp upper bound for module of the Hankel determinant |H2,3(f)| for the functions from the class Scos*. The next section deals with the sharp upper bounds of the logarithmic coefficients γ3 and γ4. Then, in addition, we found the sharp upper bound for H2,2Ff/2. To obtain these results we utilized the very useful and appropriate Lemma 2.4 of N.E. Cho et al., which gave a most accurate description for the first five coefficients of the functions from the Carathéodory’s functions class, and provided a technique for finding the maximum value of a three-variable function on a closed cuboid. All the maximum found values were checked by using MAPLE™ computer software, and we also found the extremal functions in each case. All of our most recent results are the best ones and give sharp versions of those recently published by Hacet. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
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