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Axioms
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New Developments in Geometric Function Theory, 3rd Edition
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New Developments in Geometric Function Theory, 3rd Edition

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 3302

Special Issue Editor

Dr. Georgia Irina Oros

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania
Interests: special classes of univalent functions; differential subordinations and superordinations; differential operators; integral operators; differential–integral operators
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since geometric function theory continues to be a prolific research field, following the success of the Special Issue “New Developments in Geometric Function Theory II”, comprising 14 research articles, a new volume of this Special Issue has been greenlit.

This new Special Issue, which will continue on from the framework of the preceding two Special Issues, will attempt to compile papers on the most significant recent developments in the study of complex-valued functions from the perspective of geometric function theory.

The research contributions comprising this Special Issue are expected to focus on the following subjects, among others:

  • The development of different types of differential and integral operators potentially incorporating fractional and quantum calculus aspects; presenting univalence properties for the new operators or conducting further investigations on them regarding any possible characteristics and applications in geometric function theory or related fields;
  • The introduction of new classes of analytic functions and investigations on those classes regarding different aspects, including univalence conditions, coefficient estimates, differential subordination and superordination results of any type obtained by applying means of the classical, strong or fuzzy differential subordination and superordination theories;
  • Developments within the classical, strong or fuzzy differential subordination and superordination theories;
  • Applications of special functions in geometric function theory;
  • Applications of fractional and quantum calculus aspects in geometric function theory.

New findings derived from the application of any other methodologies in the field of complex analysis are welcome to be submitted. It is hoped that by highlighting fresh research directions in geometric function theory, researchers will find motivation to continue their efforts to generate new insights in this field.

Dr. 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 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

  • analytic function
  • univalent function
  • harmonic function
  • meromorphic function
  • differential subordination
  • differential superordination
  • differential operator
  • integral operator
  • fractional operator
  • q-operator
  • special functions

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Published Papers (5 papers)

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Research

10 pages, 257 KiB  
Article
Relations of Harmonic Starlike Function Subclasses with Mittag–Leffler Function
by Naci Taşar, Fethiye Müge Sakar, Seher Melike Aydoğan and Georgia Irina Oros
Axioms 2024, 13(12), 826; https://doi.org/10.3390/axioms13120826 (registering DOI) - 26 Nov 2024
Viewed by 124
Abstract
In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag–Leffler function. The investigation reveals inclusion relations concerning harmonic γ-uniformly starlike mappings in the open unit disc, harmonic starlike functions and [...] Read more.
In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag–Leffler function. The investigation reveals inclusion relations concerning harmonic γ-uniformly starlike mappings in the open unit disc, harmonic starlike functions and harmonic convex functions, highlighting the improvements given by the results presented here on previously published outcomes. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
16 pages, 300 KiB  
Article
Third-Order Differential Subordination Features of Meromorphic Functions: Erdelyi–Kober Model Integral Operator Application
by Ibrahim S. Elshazly, Borhen Halouani, Rabha M. El-Ashwah, Alaa H. El-Qadeem and Gangadharan Murugusundaramoorthy
Axioms 2024, 13(11), 770; https://doi.org/10.3390/axioms13110770 - 6 Nov 2024
Viewed by 431
Abstract
This study is concerned with the class of p-valent meromorphic functions, represented by the series f(ζ)=ζ−p+∑k=1−p∞dkζk, with the domain characterized by [...] Read more.
This study is concerned with the class of p-valent meromorphic functions, represented by the series f(ζ)=ζ−p+∑k=1−p∞dkζk, with the domain characterized by 0<|ζ|<1. We apply an Erdelyi–Kober-type integral operator to derive two recurrence relations. From this, we draw specific conclusions on differential subordination and differential superordination. By looking into suitable classes of permitted functions, we obtain various outcomes, including results analogous to sandwich-type theorems. The operator used can provide generalizations of previous operators through specific parameter choices, thus providing more corollaries. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
13 pages, 355 KiB  
Article
Bi-Starlike Function of Complex Order Involving Mathieu-Type Series in the Shell-Shaped Region
by Ibrahim S. Elshazly, Gangadharan Murugusundaramoorthy, Borhen Halouani, Alaa H. El-Qadeem and Kaliappan Vijaya
Axioms 2024, 13(11), 747; https://doi.org/10.3390/axioms13110747 - 30 Oct 2024
Viewed by 486
Abstract
For functions of the form ϕ(ξ)=ξ+∑n=2∞cnξn, we identified two new subclasses of bi-starlike functions and bi-convex functions by using Mathieu-type series defined in the disc [...] Read more.
For functions of the form ϕ(ξ)=ξ+∑n=2∞cnξn, we identified two new subclasses of bi-starlike functions and bi-convex functions by using Mathieu-type series defined in the disc Δ={ξ∈C:|ξ|<1}. We derived constraints for |c2| and |c3|, and the subclasses are connected to the shell-shaped area. The Fekete–Szegö functional properties for the aforementioned function subclasses were also investigated. Additionally, a number of related corollaries are shown. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
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29 pages, 341 KiB  
Article
Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains
by George A. Anastassiou
Axioms 2024, 13(7), 462; https://doi.org/10.3390/axioms13070462 - 9 Jul 2024
Viewed by 1036
Abstract
In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All [...] Read more.
In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are obtained from the whole real line. The neural network operators used here are of the quasi-interpolation type: basic ones, Kantorovich-type ones, and those of the quadrature type. We provide pointwise and uniform approximations with rates. We finish with their applications. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
12 pages, 280 KiB  
Article
Generalized Bounded Turning Functions Connected with Gregory Coefficients
by Huo Tang, Zeeshan Mujahid, Nazar Khan, Fairouz Tchier and Muhammad Ghaffar Khan
Axioms 2024, 13(6), 359; https://doi.org/10.3390/axioms13060359 - 28 May 2024
Viewed by 715
Abstract
In this research article, we introduce new family RG of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for [...] Read more.
In this research article, we introduce new family RG of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for the functions belonging to this newly defined family, demonstrating their sharpness. Furthermore, we find the third Hankel determinant for functions in the class RG. Moreover, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the under-considered class RG are estimated. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
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