Special Issue "Complex Analysis"

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

Deadline for manuscript submissions: 30 November 2021.

Special Issue Editor

Prof. Dr. Andriy Bandura
E-Mail Website1 Website2
Guest Editor
Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 76019 Ivano-Frankivsk, Ukraine
Interests: entire function; analytic function; growth estimates; bounded index; bounded index in direction; bounded index in joint variables; slice holomorphic function; unit ball; polydisc; vector-valued analytic function; unit disc; value distribution

Special Issue Information

Dear Colleagues,

We are excited to launch a new Special Issue of Axioms. The central topic in the Special Issue will be “Complex Analysis and Its Applications”. Our aim is to showcase recent contributions in the many branches of both theoretical and practical studies in complex analysis, as well as 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; analytic theory of differential equations; geometric functions theory; Dirichlet series; and meromorphic functions. The Special Issue is open to receiving further related topics of complex analysis.

We highly encourage you to submit your current original research papers for inclusion in the Special Issue.

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 papers will be 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 quarterly 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 1400 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
  • Polydisc
  • Geometric function theory
  • Analytic solutions of differential equations
  • Meromorphic functions
  • Nevanlinna theory
  • Dirichlet series
  • Approximation theory in the complex plane
  • Entire curves
  • Vector-valued entire functions

Published Papers (5 papers)

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Research

Article
Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli
Axioms 2021, 10(3), 160; https://doi.org/10.3390/axioms10030160 - 26 Jul 2021
Viewed by 184
Abstract
Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ1). Notably, these results are applied to derive sufficient conditions for fA to satisfy the condition zf(z)f(z)21<1. Several previous results are extended. Full article
(This article belongs to the Special Issue Complex Analysis)
Article
Symmetry Breaking of a Time-2D Space Fractional Wave Equation in a Complex Domain
Axioms 2021, 10(3), 141; https://doi.org/10.3390/axioms10030141 - 30 Jun 2021
Viewed by 262
Abstract
(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional [...] Read more.
(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional differential operator is used together with a symmetric operator to define a new fractional symmetric operator. Then by applying the new operator, we formulate a generalized time-2D space fractional wave equation. We shall utilize the two concepts: subordination and majorization to present our results; (3) Results: we obtain different formulas of analytic solutions using the geometric analysis. The solution suggests univalent (1-1) in the open unit disk. Moreover, under certain conditions, it was starlike and dominated by a chaotic function type sine. In addition, the authors formulated a fractional time wave equation by using the Atangana–Baleanu fractional operators in terms of the Riemann–Liouville and Caputo derivatives. Full article
(This article belongs to the Special Issue Complex Analysis)
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Article
Solutions for Several Quadratic Trinomial Difference Equations and Partial Differential Difference Equations in C2
Axioms 2021, 10(2), 126; https://doi.org/10.3390/axioms10020126 - 21 Jun 2021
Viewed by 398
Abstract
This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)f(z)z1+f(z)z12=eg(z),f(z+c)2+2αf(z+c)f(z)z1+f(z)z2+f(z)z1+f(z)z22=eg(z). We establish some theorems about the forms of the finite order transcendental entire solutions of these functional equations. We also list a series of examples to explain the existence of the finite order transcendental entire solutions of such equations. Meantime, some examples show that there exists a very significant difference with the previous literature on the growth order of the finite order transcendental entire solutions. Our results show that some functional equations can admit the transcendental entire solutions with any positive integer order. These results make a few improvements of the previous theorems given by Xu and Cao, Liu and Yang. Full article
(This article belongs to the Special Issue Complex Analysis)
Article
Properties of λ-Pseudo-Starlike Functions of Complex Order Defined by Subordination
Axioms 2021, 10(2), 86; https://doi.org/10.3390/axioms10020086 - 07 May 2021
Viewed by 362
Abstract
In this paper, we defined a new class of λ-pseudo-Bazilevič functions of complex order using subordination. Various classes of analytic functions that map unit discs onto a conic domain and some classes of special functions were studied in dual. Some subordination results, inequalities for the initial Taylor–Maclaurin coefficients and the unified solution of the Fekete–Szegő problem for subclasses of analytic functions related to various conic regions, are our main results. Our main results have many applications which are presented in the form of corollaries. Full article
(This article belongs to the Special Issue Complex Analysis)
Article
Relative Growth of Series in Systems of Functions and Laplace—Stieltjes-Type Integrals
Axioms 2021, 10(2), 43; https://doi.org/10.3390/axioms10020043 - 25 Mar 2021
Viewed by 397
Abstract
For a regularly converging-in-C series A(z)=n=1anf(λnz), where f is an entire transcendental function, the asymptotic behavior of the function Mf1(MA(r)), where Mf(r)=max{|f(z)|:|z|=r}, is investigated. It is proven that, under certain conditions on the functions f, α, and the coefficients an, the equality limr+α(Mf1(MA(r)))α(r)=1 is correct. A similar result is obtained for the Laplace–Stiltjes-type integral I(r)=0a(x)f(rx)dF(x). Unresolved problems are formulated. Full article
(This article belongs to the Special Issue Complex Analysis)
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