Special Issue "Geometrical Theory of Analytic Functions"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 October 2020.

Special Issue Editor

Prof. Georgia Irina Oros
Website
Guest Editor
Department of Mathematics and Computer Science, University of Oradea, Oradea, Romania
Interests: univalent functions; harmonic functions; differential subordination and superordination; geometric theory of analytic and non-analytic functions.

Special Issue Information

Dear Colleagues,

The Special Issue devoted to the Geometric Theory of Analytic Functions will bring together the newest research achievements of scholars studying the complex-valued functions of one variable. The issue will cover all aspects of this topic, starting with special classes of univalent functions, operator-related results, studies using the theory of differential subordination and superordination, or any other techniques which can be applied in the field of complex analysis and its applications.

The Editors of this Special Issue are pleased to invite the authors to submit their original results related to analytic functions and even studies related to non-analytic functions, if any research was done comparing the two types of complex-valued functions. We await the latest results related to classic differential subordination and superordination, strong differential subordination and superordination, and fuzzy differential subordination and superordination. We believe researchers are eager to see how differential, integral, and differential–integral operators are used on the special classes of univalent functions already known or newly introduced and what their importance in the field is. This Special Issue will also publish contributions related exclusively to complex analysis and we hope to find among the results new approaches for Geometric Function Theory which could inspire further achievements in the field.

Prof. Georgia Irina Oros
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.

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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 1200 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

  • analytic function
  • univalent function
  • harmonic function
  • differential subordination
  • differential superordination
  • strong differential subordination
  • strong differential superordination
  • fuzzy differential subordination
  • fuzzy differential superordination
  • differential operator
  • integral operator
  • differential–integral operator
  • linear operator

Published Papers (7 papers)

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Research

Open AccessArticle
New Criteria for Meromorphic Starlikeness and Close-to-Convexity
Mathematics 2020, 8(5), 847; https://doi.org/10.3390/math8050847 - 23 May 2020
Abstract
The main purpose of current paper is to obtain some new criteria for meromorphic strongly starlike functions of order α and strongly close-to-convexity of order α . Furthermore, the main results presented here are compared with the previous outcomes obtained in this area. [...] Read more.
The main purpose of current paper is to obtain some new criteria for meromorphic strongly starlike functions of order α and strongly close-to-convexity of order α . Furthermore, the main results presented here are compared with the previous outcomes obtained in this area. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
Open AccessArticle
On The Third-Order Complex Differential Inequalities of ξ-Generalized-Hurwitz–Lerch Zeta Functions
Mathematics 2020, 8(5), 845; https://doi.org/10.3390/math8050845 - 23 May 2020
Abstract
In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order [...] Read more.
In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order differential subordination for a newly defined linear operator that includes ξ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating the appropriate classes of admissible functions. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
Open AccessArticle
Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator
Mathematics 2020, 8(5), 783; https://doi.org/10.3390/math8050783 - 13 May 2020
Abstract
Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + belonging to the normalized analytic function class A in the open unit disk U = z : z [...] Read more.
Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
Open AccessArticle
Starlikeness Condition for a New Differential-Integral Operator
Mathematics 2020, 8(5), 694; https://doi.org/10.3390/math8050694 - 02 May 2020
Abstract
A new differential-integral operator of the form I n f ( z ) = ( 1 λ ) S n f ( z ) + λ L n f ( z ) , z U , f A , 0 [...] Read more.
A new differential-integral operator of the form I n f ( z ) = ( 1 λ ) S n f ( z ) + λ L n f ( z ) , z U , f A , 0 λ 1 , n N is introduced in this paper, where S n is the Sălăgean differential operator and L n is the Alexander integral operator. Using this operator, a new integral operator is defined as: F ( z ) = β + γ z γ 0 z I n f ( z ) · t β + γ 2 d t 1 β , where I n f ( z ) is the differential-integral operator given above. Using a differential subordination, we prove that the integral operator F ( z ) is starlike. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
Open AccessArticle
Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space
Mathematics 2020, 8(4), 568; https://doi.org/10.3390/math8040568 - 11 Apr 2020
Abstract
This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the [...] Read more.
This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the p-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the “broom topology” type. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
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Open AccessArticle
Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative
Mathematics 2020, 8(3), 418; https://doi.org/10.3390/math8030418 - 14 Mar 2020
Cited by 1
Abstract
In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this [...] Read more.
In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
Open AccessArticle
Symmetric Conformable Fractional Derivative of Complex Variables
Mathematics 2020, 8(3), 363; https://doi.org/10.3390/math8030363 - 06 Mar 2020
Cited by 1
Abstract
It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to [...] Read more.
It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to provide a study of SCDO connected with the geometric function theory. These differential operators indicate a generalization of well known differential operator including the Sàlàgean differential operator. Our contribution is to impose two classes of symmetric differential operators in the open unit disk and to describe the further development of these operators by introducing convex linear symmetric operators. In addition, by acting these SCDOs on the class of univalent functions, we display a set of sub-classes of analytic functions having geometric representation, such as starlikeness and convexity properties. Investigations in this direction lead to some applications in the univalent function theory of well known formulas, by defining and studying some sub-classes of analytic functions type Janowski function and convolution structures. Moreover, by using the SCDO, we introduce a generalized class of Briot–Bouquet differential equations to introduce, what is called the symmetric conformable Briot–Bouquet differential equations. We shall show that the upper bound of this class is symmetric in the open unit disk. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
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