Recent Advances in Complex Analysis and Applications

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

Deadline for manuscript submissions: closed (20 October 2023) | Viewed by 11357

Special Issue Editor

Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia
Interests: geometric function theory; harmonic maps; quasiconformal maps; Hardy spaces
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex numbers and complex analysis show up everywhere in mathematics and physics. This Special Issue, “Recent Advances in Complex Analysis and Applications”, aims to provide a collection of high-quality original research articles and surveys in the field of Complex Analysis and Applications. Of particular interest are contributions addressing topics including, but not limited to: geometric function theory, quasiconformal harmonic maps, convex and starlike univalent functions, Lipschitz continuity and smoothness up to the boundary of solutions of the hyperbolic Poisson equation, spatial versions of Kellogg’s theorem, harmonic maps and maps which satisfy PDEs of second order, properties of mappings admitting general Poisson representations, Hardy spaces, extremal problems related to harmonic maps, etc.

Original articles reporting recent progress as well as survey articles are also sought.

Prof. Dr. Miodrag Mateljevic
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.

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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

  • geometric function theory
  • harmonic maps
  • Hardy spaces
  • quasiconformal maps
  • univalent functions
  • harmonic analysis
  • PDE

Published Papers (12 papers)

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Research

14 pages, 280 KiB  
Article
Further Geometric Properties of the Barnes–Mittag-Leffler Function
by Abdulaziz Alenazi and Khaled Mehrez
Axioms 2024, 13(1), 12; https://doi.org/10.3390/axioms13010012 - 24 Dec 2023
Viewed by 774
Abstract
In this paper, we find sufficient conditions to be imposed on the parameters of a class of functions related to the Barnes–Mittag-Leffler function that allow us to conclude that it possesses certain geometric properties (such as starlikeness, uniformly starlike (convex), strongly starlike (convex), [...] Read more.
In this paper, we find sufficient conditions to be imposed on the parameters of a class of functions related to the Barnes–Mittag-Leffler function that allow us to conclude that it possesses certain geometric properties (such as starlikeness, uniformly starlike (convex), strongly starlike (convex), convexity, and close-to-convexity) in the unit disk. The key tools in some of our proofs are the monotonicity properties of a certain class of functions related to the gamma function. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
15 pages, 328 KiB  
Article
Toeplitz Operators on Fock Space over Cn with Invariant Symbols under the Action of the Unit Circle
by Carlos González-Flores, Luis Alfredo Dupont-García, Raquiel Rufino López-Martínez and Francisco Gabriel Hérnandez-Zamora
Axioms 2023, 12(12), 1080; https://doi.org/10.3390/axioms12121080 - 25 Nov 2023
Viewed by 758
Abstract
The first goal of this paper is to find a representation of the Fock space on Cn in terms of the weighted Bergman spaces of the projective spaces CPn1; i.e., every function in the Fock space can be [...] Read more.
The first goal of this paper is to find a representation of the Fock space on Cn in terms of the weighted Bergman spaces of the projective spaces CPn1; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on CPn1. Also, we study the C* algebras generated by Toeplitz operators where the symbols are taken from the following two families of functions: Firstly, the symbols depend on the moment map associated with the unit circle, and secondly, the symbols are invariant under the same action. Moreover, we analyze the commutative relations between these algebras, and we apply these results to find new commutative Banach algebras generated by Toeplitz operators on Fock space of Cn. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
11 pages, 289 KiB  
Article
Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values
by Richard D. Carmichael
Axioms 2023, 12(11), 1036; https://doi.org/10.3390/axioms12111036 - 06 Nov 2023
Viewed by 736
Abstract
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1p<2, if the boundary value is in the vector-valued [...] Read more.
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1p<2, if the boundary value is in the vector-valued Lp,1p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2p. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1p. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
13 pages, 324 KiB  
Article
Lipschitz Continuity for Harmonic Functions and Solutions of the α¯-Poisson Equation
by Miodrag Mateljević, Nikola Mutavdžić and Adel Khalfallah
Axioms 2023, 12(10), 998; https://doi.org/10.3390/axioms12100998 - 23 Oct 2023
Cited by 2 | Viewed by 1051
Abstract
In this paper we investigate the solutions of the so-called α¯-Poisson equation in the complex plane. In particular, we will give sufficient conditions for Lipschitz continuity of such solutions. We also review some recently obtained results. As a corollary, we can [...] Read more.
In this paper we investigate the solutions of the so-called α¯-Poisson equation in the complex plane. In particular, we will give sufficient conditions for Lipschitz continuity of such solutions. We also review some recently obtained results. As a corollary, we can restate results for harmonic and (p,q)-harmonic functions. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
15 pages, 297 KiB  
Article
Quasiconformal Homeomorphisms Explicitly Determining the Basic Curve Quasi-Invariants
by Samuel L. Krushkal
Axioms 2023, 12(10), 944; https://doi.org/10.3390/axioms12100944 - 30 Sep 2023
Viewed by 764
Abstract
The classical Belinskii theorem implies that any sufficiently regular function μ(z) on the extended complex plane C^ with a small C1+α norm generates via the two-dimensional Cauchy integral a quasiconformal automorphism w of C^ with [...] Read more.
The classical Belinskii theorem implies that any sufficiently regular function μ(z) on the extended complex plane C^ with a small C1+α norm generates via the two-dimensional Cauchy integral a quasiconformal automorphism w of C^ with the Beltrami coefficient μ˜=μ+O(μ2). We consider μ supported in arbitrary bounded quasiconformal disks and show that under appropriate assumptions of μ, this automorphism explicitly provides the basic curvelinear quasi-invariants associated with conformal and quasiconformal maps, advancing an old problem of quasiconformal analysis. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
13 pages, 293 KiB  
Article
Zalcman Functional and Majorization Results for Certain Subfamilies of Holomorphic Functions
by Muhammad Ghafar Khan, Bilal Khan, Ferdous M. O. Tawfiq and Jong-Suk Ro
Axioms 2023, 12(9), 868; https://doi.org/10.3390/axioms12090868 - 08 Sep 2023
Cited by 2 | Viewed by 716
Abstract
In this paper, we investigate sharp coefficient functionals, like initial four sharp coefficient bounds, sharp Fekete–Szegö functionals, and, for n=1 and 2, sharp Zalcman functionals are evaluated for class of functions associated with tangent functions. Furthermore, we provide some majorization results [...] Read more.
In this paper, we investigate sharp coefficient functionals, like initial four sharp coefficient bounds, sharp Fekete–Szegö functionals, and, for n=1 and 2, sharp Zalcman functionals are evaluated for class of functions associated with tangent functions. Furthermore, we provide some majorization results for some non-vanishing holomorphic functions, whose ratios are related to various domains in the open unit disk. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
15 pages, 319 KiB  
Article
Sharp Coefficient Bounds for a Subclass of Bounded Turning Functions with a Cardioid Domain
by Lei Shi, Hari Mohan Srivastava, Nak Eun Cho and Muhammad Arif
Axioms 2023, 12(8), 775; https://doi.org/10.3390/axioms12080775 - 10 Aug 2023
Cited by 1 | Viewed by 680
Abstract
In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a [...] Read more.
In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
11 pages, 306 KiB  
Article
Applications of Shell-like Curves Connected with Fibonacci Numbers
by Ala Amourah, Ibtisam Aldawish, Basem Aref Frasin and Tariq Al-Hawary
Axioms 2023, 12(7), 639; https://doi.org/10.3390/axioms12070639 - 28 Jun 2023
Viewed by 759
Abstract
We introduce a new subclass JΣη,δ,μ(p˜) of bi-univalent functions, defined by shell-like curves connected with Fibonacci numbers. Our main results in this paper include estimates of the Taylor–Maclaurin coefficients a2 and [...] Read more.
We introduce a new subclass JΣη,δ,μ(p˜) of bi-univalent functions, defined by shell-like curves connected with Fibonacci numbers. Our main results in this paper include estimates of the Taylor–Maclaurin coefficients a2 and a3 for functions in this subclass, as well as solutions to Fekete–Szegö functional problems. We also show novel outcomes resulting from the specialization of the parameters used in our main results. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
20 pages, 346 KiB  
Article
Equivalent Base Expansions in the Space of Cliffordian Functions
by Mohra Zayed and Gamal Hassan
Axioms 2023, 12(6), 544; https://doi.org/10.3390/axioms12060544 - 31 May 2023
Cited by 3 | Viewed by 674
Abstract
Intensive research efforts have been dedicated to the extension and development of essential aspects that resulted in the theory of one complex variable for higher-dimensional spaces. Clifford analysis was created several decades ago to provide an elegant and powerful generalization of complex analyses. [...] Read more.
Intensive research efforts have been dedicated to the extension and development of essential aspects that resulted in the theory of one complex variable for higher-dimensional spaces. Clifford analysis was created several decades ago to provide an elegant and powerful generalization of complex analyses. In this paper, first, we derive a new base of special monogenic polynomials (SMPs) in Fréchet–Cliffordian modules, named the equivalent base, and examine its convergence properties for several cases according to certain conditions applied to related constituent bases. Subsequently, we characterize its effectiveness in various convergence regions, such as closed balls, open balls, at the origin, and for all entire special monogenic functions (SMFs). Moreover, the upper and lower bounds of the order of the equivalent base are determined and proved to be attainable. This work improves and generalizes several existing results in the complex and Clifford context involving the convergence properties of the product and similar bases. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
12 pages, 284 KiB  
Article
Partial Sums of the Normalized Le Roy-Type Mittag-Leffler Function
by Basem Aref Frasin and Luminiţa-Ioana Cotîrlă
Axioms 2023, 12(5), 441; https://doi.org/10.3390/axioms12050441 - 29 Apr 2023
Viewed by 696
Abstract
Recently, some researchers determined lower bounds for the normalized version of some special functions to its sequence of partial sums, e.g., Struve and Dini functions, Wright functions and Miller–Ross functions. In this paper, we determine lower bounds for the normalized Le Roy-type Mittag-Leffler [...] Read more.
Recently, some researchers determined lower bounds for the normalized version of some special functions to its sequence of partial sums, e.g., Struve and Dini functions, Wright functions and Miller–Ross functions. In this paper, we determine lower bounds for the normalized Le Roy-type Mittag-Leffler function Fα,βγ(z)=z+n=1Anzn+1, where An=ΓβΓα(n1)+βγ and its sequence of partial sums (Fα,βγ(z))m(z)=z+n=1mAnzn+1. Several examples of the main results are also considered. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
9 pages, 276 KiB  
Article
Some New Sufficient Conditions on p-Valency for Certain Analytic Functions
by Lei Shi, Muhammad Arif, Syed Zakar Hussain Bukhari and Malik Ali Raza
Axioms 2023, 12(3), 295; https://doi.org/10.3390/axioms12030295 - 13 Mar 2023
Cited by 1 | Viewed by 920
Abstract
In the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be p-valent functions. This work also extends the findings of Nunokawa and others. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
13 pages, 296 KiB  
Article
A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions
by Ala Amourah, Abdullah Alsoboh, Osama Ogilat, Gharib Mousa Gharib, Rania Saadeh and Maha Al Soudi
Axioms 2023, 12(2), 128; https://doi.org/10.3390/axioms12020128 - 28 Jan 2023
Cited by 20 | Viewed by 1457
Abstract
Three subclasses of analytic and bi-univalent functions are introduced through the use of qGegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are [...] Read more.
Three subclasses of analytic and bi-univalent functions are introduced through the use of qGegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads to a number of new results. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)
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