Advances in Geometric Function Theory and Related Topics

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

Deadline for manuscript submissions: 30 November 2024 | Viewed by 1947

Special Issue Editors


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Guest Editor
Department of Statistics. Forecasts. Mathematics, Faculty of Economics and Business Administration, Babes-Bolyai University, Cluj-Napoca, Romania
Interests: geometric function theory and its applications; differential subordination and superordination, complex analysis; univalent functions; harmonic functions

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Guest Editor
Faculty of Mathematics and Computer Science, Babes-Bolyai University, 1 M. Kogalniceanu Street, 400084 Cluj-Napoca,, Romania
Interests: geometric function theory, complex analysis; univalent and multivalent functions; harmonic functions; differential operators
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania
Interests: geometric function theory and its applications; differential subordination and superordination, complex analysis, univalent functions, special functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In this Special Issue, devoted to the topic of Geometric Function Theory and Related Topics, we aim to gather the latest developments in research concerning complex-valued functions from the point of view of the geometric function theory.

Geometric function theory (GFT) is one of the most important branches of complex analysis, which seeks to relate the analytic properties of conformal maps to geometric properties of their images, and it has many applications in various fields of mathematics, including special functions, dynamical systems, analytic number theory, fractional calculus, and probability distributions.

The purpose of this Special Issue is to solicit original research and review articles focusing on the latest developments in this research area.

We hope that new lines of research associated with the geometric function theory will be highlighted, and that new and exciting results will boost the development of this field.

In this Special Issue, original research articles and reviews are welcome. Research areas may include, but not limited to, the following:

  • Differential and integral operators;
  • Univalent, bi-univalent, and multivalent functions;
  • Analysis of metric spaces;
  • Value distribution theory;
  • Differential subordinations and superordinations;
  • Applications of special functions in geometric functions theory;
  • Entire and meromorphic functions;
  • Fuzzy differential subordinations and superordinations;
  • Generalized function theory;
  • Quantum calculus and its applications in geometric function theory;
  • Approximation theory;
  • Harmonic univalent functions;
  • Geometric function theory in several complex variables.

We look forward to receiving your contributions.

Dr. Páll-Szabó Ágnes-Orsolya
Prof. Dr. Grigore Stefan Salagean
Prof. Dr. Teodor Bulboaca
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. 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

  • univalent functions
  • bi-univalent functions
  • harmonic complex functions
  • differential operators
  • integral operator
  • fractional operator
  • coefficient estimates
  • differential subordination
  • differential superordination
  • quantum calculus
  • fuzzy differential subordinations and superordinations
  • several complex variables

Published Papers (2 papers)

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Research

19 pages, 289 KiB  
Article
Certain New Applications of Symmetric q-Calculus for New Subclasses of Multivalent Functions Associated with the Cardioid Domain
by Hari M. Srivastava, Daniel Breaz, Shahid Khan and Fairouz Tchier
Axioms 2024, 13(6), 366; https://doi.org/10.3390/axioms13060366 - 29 May 2024
Viewed by 294
Abstract
In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We [...] Read more.
In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies. Full article
(This article belongs to the Special Issue Advances in Geometric Function Theory and Related Topics)
19 pages, 521 KiB  
Article
Subclasses of Analytic Functions Subordinated to the Four-Leaf Function
by Saravanan Gunasekar, Baskaran Sudharsanan, Musthafa Ibrahim and Teodor Bulboacă
Axioms 2024, 13(3), 155; https://doi.org/10.3390/axioms13030155 - 27 Feb 2024
Cited by 1 | Viewed by 1106
Abstract
The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass A4r,s of analytic functions related to the four-leaf domain, [...] Read more.
The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass A4r,s of analytic functions related to the four-leaf domain, to increase the adaptability of our investigation. The initial findings are the bound estimates for the coefficients |an|, n=2,3,4,5, among which the bound of |a2| is sharp. Also, we include the sharp-function illustration. Additionally, we obtain the upper-bound estimate for the second Hankel determinant for this subclass as well as those for the Fekete–Szegő functional. Finally, for these subclasses, we provide an estimation of the Krushkal inequality for the function class A4r,s. Full article
(This article belongs to the Special Issue Advances in Geometric Function Theory and Related Topics)
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