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Mathematics
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Advances in Complex Analysis and Application
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Advances in Complex Analysis and Application

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 1231

Special Issue Editor

Prof. Dr. Mihaela Vajiac

E-Mail Website
Guest Editor
Schmid College of Science and Technology, Chapman University, One University Drive Orange, Orange, CA 92866, USA
Interests: complex and hypercomplex analysis; differential geometry; symplectic geometry; integrable systems

Special Issue Information

Dear Colleagues,

"Advances in Complex Analysis and Application" is a comprehensive study that delves into the latest developments and applications in the field of complex analysis. It explores new methods, techniques, and theories that have emerged in the field, expanding its potential applications in various scientific and technological domains. This Special Issue includes a wide range of topics such as harmonic analysis, potential theory, several complex variables, and operator theory. This publication serves as a valuable resource for researchers, scholars, and students interested in complex analysis and its contemporary applications.

The topics of interest for this Special Issue include but are not limited to:

  • Complex Dynamical Systems
  • Complex Variables in Quantum Field Theory
  • Harmonic Analysis and Partial Differential Equations
  • Advances in Complex Geometry
  • Operator Theory in Complex Analysis
  • Complex Networks
  • Nonlinear Analysis and Complex Systems
  • Complex Analysis and Mathematical Physics
  • Complex Analysis in Number Theory
  • Complex Analysis and Machine Learning

We believe that this Special Issue will serve as a platform for further advancements in complex analysis. We look forward to receiving your submissions and contributions to this important area of research.

Prof. Dr. Mihaela Vajiac
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • complex analysis
  • complex variables
  • complex functions
  • mathematical physics
  • harmonic analysis
  • potential theory
  • several complex variables
  • geometric function theory
  • complex dynamics
  • Riemann surfaces
  • complex plane
  • advanced calculus

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (2 papers)

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Research

15 pages, 2401 KiB  
Article
Some Properties and Graphical Applications of a New Subclass of Harmonic Functions Defined by a Differential Inequality
by Sibel Yalçın, Hasan Bayram and Georgia Irina Oros
Mathematics 2024, 12(15), 2338; https://doi.org/10.3390/math12152338 - 26 Jul 2024
Viewed by 447
Abstract
This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of [...] Read more.
This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrates that this subclass remains stable under the convolution operation applied to its members. In addition, in the last section, images of the unit disk under some functions of this class are given. Full article
(This article belongs to the Special Issue Advances in Complex Analysis and Application)
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13 pages, 1417 KiB  
Article
A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via q̧-Calculus
by Ala Amourah, Abdullah Alsoboh, Daniel Breaz and Sheza M. El-Deeb
Mathematics 2024, 12(11), 1735; https://doi.org/10.3390/math12111735 - 3 Jun 2024
Cited by 1 | Viewed by 539
Abstract
Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. [...] Read more.
Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on |α2| and |α3| coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. Full article
(This article belongs to the Special Issue Advances in Complex Analysis and Application)
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