Advances on Complex Analysis

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 19114

Special Issue Editors

Department of Computing, Mathematics and Electronics, "1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania
Interests: complex analysis; univalent functions; special functions
Special Issues, Collections and Topics in MDPI journals
1. Department of Informatics, Mathematicsand Electronics, Faculty of Science and Engineering, "1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania
2. Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
Interests: systems and control; time-varying systems; dynamical systems; difference equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The purpose of this Special Issue is to gather contributions on the most recent advances in the mathematical theory of complex analysis and its applications to the fields of physics and engineering as well as other areas of mathematics, both pure and applied. We would like to include recent developments in several branches of complex analysis, including geometric function theory, analytic number theory, differential subordination and superordination, function algebras, and quantum calculus and its applications in geometric function theory.

Our goal is to stimulate continuing efforts toward developing new results on these topics. To help us meet this goal, we invite authors to submit original research articles as well as high-quality review articles that reflect the Special Issue theme.

Prof. Valer-Daniel Breaz
Dr. Ioan-Lucian Popa
Guest Editors

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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

  • Complex polynomials
  • Analytic and harmonic univalent functions 
  • Meromorphic univalent functions 
  • Differential subordination and superordination 
  • Special functions and its applications in geometric function theory
  • Quantum calculus and its applications in geometric function theory 
  • Operators on function spaces

Published Papers (14 papers)

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Research

16 pages, 683 KiB  
Article
On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators
by Ovidiu Bagdasar, Minsi Chen, Vasile Drăgan, Ivan Ganchev Ivanov and Ioan-Lucian Popa
Mathematics 2023, 11(5), 1244; https://0-doi-org.brum.beds.ac.uk/10.3390/math11051244 - 04 Mar 2023
Cited by 2 | Viewed by 1136
Abstract
Horadam sequence is a general recurrence of second order in the complex plane, depending on four complex parameters (two initial values and two recurrence coefficients). These sequences have been investigated over more than 60 years, but new properties and applications are still being [...] Read more.
Horadam sequence is a general recurrence of second order in the complex plane, depending on four complex parameters (two initial values and two recurrence coefficients). These sequences have been investigated over more than 60 years, but new properties and applications are still being discovered. Small parameter variations may dramatically impact the sequence orbits, generating numerous patterns: periodic, convergent, divergent, or dense within one dimensional curves. Here we explore Horadam sequences whose orbit is dense within a 2D region of the complex plane, while the complex argument is uniformly distributed in an interval. This enables the design of a pseudo-random number generator (PRNG) for the uniform distribution, for which we test periodicity, correlation, Monte Carlo estimation of π, and the NIST battery of tests. We then calculate the probability distribution of the radii of the sequence terms of Horadam sequences. Finally, we propose extensions of these results for generalized Horadam sequences of third order. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
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12 pages, 303 KiB  
Article
Admissible Classes of Multivalent Meromorphic Functions Defined by a Linear Operator
by Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi and Nicoleta Breaz
Mathematics 2022, 10(21), 4136; https://0-doi-org.brum.beds.ac.uk/10.3390/math10214136 - 05 Nov 2022
Viewed by 790
Abstract
The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For [...] Read more.
The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For that, the appropriate classes of admissible functions are first defined. Based on these classes, we obtain some differential subordination and superordination results for multivalent meromorphic functions, analytic in the punctured unit disc, related to a linear operator ρ,τp(ν), for τ>0,ν,ρC, such that Re(ρν)0, Re(ν)>τp,(pN). Moreover, taking into account both subordination and superordination results, we derive a sandwich-type theorem. The connection with some other known results and an example are also provided. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
12 pages, 1172 KiB  
Article
On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter
by Dorin Andrica and Ovidiu Bagdasar
Mathematics 2022, 10(18), 3334; https://0-doi-org.brum.beds.ac.uk/10.3390/math10183334 - 14 Sep 2022
Cited by 1 | Viewed by 1001
Abstract
We explore the dynamics of the sequence of Kasner quadrilaterals (AnBnCnDn)n0 defined via a complex parameter α. We extend the results concerning Kasner triangles with a fixed complex parameter obtained [...] Read more.
We explore the dynamics of the sequence of Kasner quadrilaterals (AnBnCnDn)n0 defined via a complex parameter α. We extend the results concerning Kasner triangles with a fixed complex parameter obtained in earlier works and determine the values of α for which the generated dynamics are convergent, divergent, periodic, or dense. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
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12 pages, 275 KiB  
Article
Close-to-Convexity of q-Bessel–Wright Functions
by Muhey U. Din, Mohsan Raza, Qin Xin, Sibel Yalçin and Sarfraz Nawaz Malik
Mathematics 2022, 10(18), 3322; https://0-doi-org.brum.beds.ac.uk/10.3390/math10183322 - 13 Sep 2022
Cited by 1 | Viewed by 1059
Abstract
In this paper, we aim to find sufficient conditions for the close-to-convexity of q-Bessel–Wright functions with respect to starlike functions, such as z1z,z1z2, and log(1z) are [...] Read more.
In this paper, we aim to find sufficient conditions for the close-to-convexity of q-Bessel–Wright functions with respect to starlike functions, such as z1z,z1z2, and log(1z) are in the open unit disc. Some consequences related to our main results are also included. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
10 pages, 1231 KiB  
Article
On Lemniscate Starlikeness of the Solution of General Differential Equations
by Saiful R. Mondal
Mathematics 2022, 10(18), 3254; https://0-doi-org.brum.beds.ac.uk/10.3390/math10183254 - 07 Sep 2022
Cited by 3 | Viewed by 974
Abstract
In this article, we derived conditions on the coefficient functions a(z) and b(z) of the differential equations [...] Read more.
In this article, we derived conditions on the coefficient functions a(z) and b(z) of the differential equations y(z)+a(z)y(z)+b(z)y(z)=0 and z2y(z)+a(z)zy(z)+b(z)y(z)=0, such their solution f(z) with normalization f(0)=0=f(0)1 is starlike in the lemniscate domain, equivalently zf(z)/f(z)1+z. We provide several examples with graphical presentations for a clear view of the obtained results. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
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13 pages, 312 KiB  
Article
Some Geometrical Results Associated with Secant Hyperbolic Functions
by Isra Al-Shbeil, Afis Saliu, Adriana Cătaş, Sarfraz Nawaz Malik and Semiu Oladipupo Oladejo
Mathematics 2022, 10(15), 2697; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152697 - 29 Jul 2022
Cited by 11 | Viewed by 1029
Abstract
In this paper, we examine the differential subordination implication related with the Janowski and secant hyperbolic functions. Furthermore, we explore a few results, for example, the necessary and sufficient condition in light of the convolution concept, growth and distortion bounds, radii of starlikeness [...] Read more.
In this paper, we examine the differential subordination implication related with the Janowski and secant hyperbolic functions. Furthermore, we explore a few results, for example, the necessary and sufficient condition in light of the convolution concept, growth and distortion bounds, radii of starlikeness and partial sums related to the class Ssech. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
10 pages, 298 KiB  
Article
An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials
by Ala Amourah, Basem Aref Frasin and Tamer M. Seoudy
Mathematics 2022, 10(14), 2462; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142462 - 15 Jul 2022
Cited by 17 | Viewed by 1167
Abstract
The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each [...] Read more.
The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each of these bi-univalent function classes, we have derived and explored estimates of the Taylor coefficients a2 and a3 and Fekete-Szegö functional problems for functions belonging to these new subclasses. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
14 pages, 327 KiB  
Article
Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator
by Asma Alharbi, Gangadharan Murugusundaramoorthy and Sheza. M. El-Deeb
Mathematics 2022, 10(13), 2241; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132241 - 26 Jun 2022
Cited by 4 | Viewed by 1028
Abstract
We defined two new subclasses of analytic bi-univalent function class Σ, in the open unit disk related with the Sălăgean–Erdély–Kober operator. The bounds on initial coefficients |a2|,|a3| and |a4| for the [...] Read more.
We defined two new subclasses of analytic bi-univalent function class Σ, in the open unit disk related with the Sălăgean–Erdély–Kober operator. The bounds on initial coefficients |a2|,|a3| and |a4| for the functions in these new subclasses of Σ are investigated. Using the estimates of coefficients a2,a3, we also discuss the Fekete-Szegö inequality results for the function classes defined in this paper. Relevant connections of these results, presented here as corollaries, are new and not studied in association with Sălăgean-Erdély–Kober operator for the subclasses defined earlier. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
26 pages, 997 KiB  
Article
A Note on Bell-Based Apostol-Type Frobenius-Euler Polynomials of Complex Variable with Its Certain Applications
by Noor Alam, Waseem Ahmad Khan and Cheon Seoung Ryoo
Mathematics 2022, 10(12), 2109; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122109 - 17 Jun 2022
Cited by 11 | Viewed by 1162
Abstract
In this paper, we introduce new class of Bell-based Apostol-type Frobenius–Euler polynomials and investigate some properties of these polynomials. We derive some explicit and implicit summation formulas and their symmetric identities by using different analytical means and applying generating functions of generalized Apostol-type [...] Read more.
In this paper, we introduce new class of Bell-based Apostol-type Frobenius–Euler polynomials and investigate some properties of these polynomials. We derive some explicit and implicit summation formulas and their symmetric identities by using different analytical means and applying generating functions of generalized Apostol-type Frobenius-Euler polynomials and Bell-based Apostol-type Frobenius-Euler polynomials. In particular, parametric kinds of the Bell-based Apostol-type Frobenius-Euler polynomials are introduced and some of their algebraic and analytical properties are established. In addition, illustrative examples of these families of polynomials are shown, focusing on their numerical values and piloting some beautiful computer-aided graphs of them. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
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19 pages, 333 KiB  
Article
Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions of Bounded Turning Associated with Petal-Shaped Domain
by Lei Shi, Muhammad Arif, Ayesha Rafiq, Muhammad Abbas and Javed Iqbal
Mathematics 2022, 10(11), 1939; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111939 - 06 Jun 2022
Cited by 11 | Viewed by 1238
Abstract
The purpose of this article is to obtain the sharp estimates of the first four initial logarithmic coefficients for the class BTs of bounded turning functions associated with a petal-shaped domain. Further, we investigate the sharp estimate of Fekete-Szegö inequality, Zalcman inequality [...] Read more.
The purpose of this article is to obtain the sharp estimates of the first four initial logarithmic coefficients for the class BTs of bounded turning functions associated with a petal-shaped domain. Further, we investigate the sharp estimate of Fekete-Szegö inequality, Zalcman inequality on the logarithmic coefficients and the Hankel determinant H2,1Ff/2 and H2,2Ff/2 for the class BTs with the determinant entry of logarithmic coefficients. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
8 pages, 252 KiB  
Article
Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative
by Abdel Moneim Y. Lashin, Badriah Maeed Algethami and Abeer O. Badghaish
Mathematics 2022, 10(1), 105; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010105 - 29 Dec 2021
Cited by 1 | Viewed by 977
Abstract
In this paper, the Jackson q-derivative is used to investigate two classes of analytic functions in the open unit disc. The coefficient conditions and inclusion properties of the functions in these classes are established by convolution methods. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
11 pages, 253 KiB  
Article
The Study of the New Classes of m-Fold Symmetric bi-Univalent Functions
by Daniel Breaz and Luminiţa-Ioana Cotîrlă
Mathematics 2022, 10(1), 75; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010075 - 27 Dec 2021
Cited by 12 | Viewed by 2087
Abstract
In this paper, we introduce three new subclasses of m-fold symmetric holomorphic functions in the open unit disk U, where the functions f and f1 are m-fold symmetric holomorphic functions in the open unit disk. We denote these classes of [...] Read more.
In this paper, we introduce three new subclasses of m-fold symmetric holomorphic functions in the open unit disk U, where the functions f and f1 are m-fold symmetric holomorphic functions in the open unit disk. We denote these classes of functions by FSΣ,mp,q,s(d), FSΣ,mp,q,s(e) and FSΣ,mp,q,s,h,r. As the Fekete-Szegö problem for different classes of functions is a topic of great interest, we study the Fekete-Szegö functional and we obtain estimates on coefficients for the new function classes. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
9 pages, 253 KiB  
Article
Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials
by Abdel Moneim Y. Lashin, Abeer O. Badghaish and Amani Z. Bajamal
Mathematics 2021, 9(24), 3188; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243188 - 10 Dec 2021
Cited by 2 | Viewed by 1756
Abstract
In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated. [...] Read more.
In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
14 pages, 323 KiB  
Article
Certain Integral Operators of Analytic Functions
by Alina Alb Lupaş and Loriana Andrei
Mathematics 2021, 9(20), 2586; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202586 - 14 Oct 2021
Cited by 3 | Viewed by 1074
Abstract
In this paper, two new integral operators are defined using the operator DRλm,n, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators [...] Read more.
In this paper, two new integral operators are defined using the operator DRλm,n, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator DRλm,n are also obtained. Full article
(This article belongs to the Special Issue Advances on Complex Analysis)
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