Submit to Special Issue Submit Abstract to Special Issue Review for Symmetry Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Symmetry in Complex Analysis Operators Theory

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Benefits of Publishing in a Special Issue
Published Papers

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 3396

Share This Special Issue

Special Issue Editor

Dr. Daciana Alina Alb Lupas

E-Mail Website
Guest Editor

Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, Universitatii Street, 410087 Oradea, Romania
Interests: topological algebra; geometric function theory; inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Symmetry, entitled “Symmetry in Complex Analysis Operators Theory”, is addressed to researchers in the complex analysis domain. We aim to cover all aspects of this topic, including special classes of univalent functions, operator-related results, the theory of differential subordination and superordination, or any other techniques which can be applied in the field of complex analysis and its application to evaluate the symmetric properties of a studied object.

In particular, we seek to exchange ideas among eminent mathematicians from many parts of the world, with a particular focus on geometric function theory. We intend to boost the cooperation among mathematicians working on a broad variety of pure and applied mathematical areas.

This publication will cover the wide area of applications in which the geometric function theory plays an important role. This ubiquity has resulted in this theory exercising a strong influence on everyday life, as new tools have been developed and achieved revolutionary research results, bringing scientists even closer to exact sciences.

Dr. Daciana Alina Alb Lupas
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 250 words) can be sent to the Editorial Office for assessment.

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. Symmetry 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
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

Benefits of Publishing in a Special Issue

Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (7 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

33 pages, 458 KB

Open AccessArticle

Symmetric Analytic Functions on Banach Spaces Associated with the Cantor Set

by Iryna Chernega, Roman Dmytryshyn, Zoriana Novosad, Serhii Sharyn and Andriy Zagorodnyuk

Symmetry 2026, 18(5), 716; https://doi.org/10.3390/sym18050716 - 23 Apr 2026

Viewed by 194

Abstract

We consider Banach spaces

ℓ_{p} (C),

1 \leq p < \infty,

where the index set

C

is the classical Cantor set and study various groups of symmetries of

ℓ_{p} (C),

associated with the [...] Read more.

We consider Banach spaces

ℓ_{p} (C),

1 \leq p < \infty,

where the index set

C

is the classical Cantor set and study various groups of symmetries of

ℓ_{p} (C),

associated with the binary representation of

C .

The main purpose of the paper is the investigation of polynomials on

ℓ_{p} (C)

that are symmetric (i.e., invariant) with respect to the constructed groups

G .

We are interested in finding systems of generators of algebras of G-symmetric polynomials for different groups G and we discuss possible applications of G-symmetric polynomials to highly composite physical systems. The generators are useful for descriptions of spectra of algebras of G-symmetric analytic functions on

ℓ_{p} (C),

and for the construction of some nontrivial complex homomorphisms of these algebras. Finally, we establish the topological transitivity and hypercyclicity of some shift-like operators on

ℓ_{p} (C)

and its subspaces, and translation operators on algebras of symmetric analytic functions on

ℓ_{p} (C) .

Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

► Show Figures

Figure 1

18 pages, 303 KB

Open AccessArticle

Symmetric Properties of Janowski-Type q-Harmonic Close-to-Convex Functions

by Yusra Taj, Sarfraz Nawaz Malik and Alina Alb Lupaş

Symmetry 2026, 18(5), 702; https://doi.org/10.3390/sym18050702 - 22 Apr 2026

Viewed by 236

Abstract

We introduce and study a new subclass of Janowski-type harmonic close-to-convex functions in the open unit disk defined via the Jackson q-derivative operator. The structure of the operator naturally reflects certain symmetric properties in the analytic representation of the considered harmonic mappings. By applying subordination techniques, we establish sufficient conditions for sense-preserving close-to-convexity and distortion estimates. The extreme points of the class are determined, and its topological properties are examined, showing that the class is convex and compact. We further obtain the radius of starlikeness and prove that the class is closed under convolution. Moreover, as

q \to 1^{-}

, the operator reduces to the classical derivative, and our results recover several known results in the existing literature, demonstrating that the present work extends and generalizes earlier findings. Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

19 pages, 303 KB

Open AccessArticle

Uniform Approximation by Rational Functions with Prescribed Poles: Operator-Theoretic Perspective and Symmetries

by Carlo Cattani

Symmetry 2026, 18(4), 665; https://doi.org/10.3390/sym18040665 - 16 Apr 2026

Viewed by 336

Abstract

In this paper, the uniform approximation of continuous functions on

[0, 1]

by rational functions with prescribed poles and bounded multiplicities is studied. A classical theorem of Fichera characterizes density in

C ([0, 1])

through [...] Read more.

In this paper, the uniform approximation of continuous functions on

[0, 1]

by rational functions with prescribed poles and bounded multiplicities is studied. A classical theorem of Fichera characterizes density in

C ([0, 1])

through the divergence of a conformally invariant series involving the pole distribution. A modern reformulation of this result is developed and it is given an operator-theoretic interpretation in which the approximation property is equivalent to cyclicity and to the absence of nontrivial invariant subspaces in an associated Hardy-space model. In this framework, the classical Blaschke condition emerges as the fundamental obstruction to density, linking rational approximation to the structure of model spaces and non-selfadjoint operator algebras. The density criterion is interpreted in terms of symmetry: divergence corresponds to a balanced distribution of poles compatible with the conformal geometry of the slit domain, while convergence induces symmetry breaking and the emergence of invariant structures. Numerical models illustrate the sharpness of the criterion and provide a concrete manifestation of the Blaschke obstruction and cyclicity mechanism. This new approach places Fichera’s theorem within a broader operator-theoretic and spectral framework, connecting classical approximation theory with Hardy spaces, invariant subspace theory, and modern rational approximation methods. Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

32 pages, 2268 KB

Open AccessArticle

Symmetry-Driven Multi-Objective Dream Optimization for Intelligent Healthcare Resource Management and Emergency Response

by Ashraf A. Abu-Ein, Ahmed R. El-Saeed, Obaida M. Al-Hazaimeh, Hanin Ardah, Gaber Hassan, Mohammed Tawfik and Islam S. Fathi

Symmetry 2026, 18(3), 530; https://doi.org/10.3390/sym18030530 - 20 Mar 2026

Viewed by 467

Abstract

Structural symmetry appears as a natural feature in both optimal solution landscapes and hospital scheduling behaviors, representing an inherent balance that can be deliberately leveraged to improve how quickly algorithms converge and how reliably systems perform in intricate healthcare optimization contexts. Managing hospital resources is a multifaceted challenge that requires simultaneously addressing several competing goals, such as reducing costs, improving patient experiences, making the most of available resources, distributing staff workload fairly, and strengthening readiness for emergencies. Traditional optimization approaches frequently struggle to cope with the complexity and ever-changing nature of modern healthcare environments. To address this gap, this study introduces a novel Multi-Objective Dream Optimization Algorithm (MO-DOA) tailored for smart healthcare resource management, which adapts a biologically inspired optimization framework to meet the specific demands of healthcare settings. The MO-DOA is built around three core mechanisms: a foundational memory component that retains high-quality solutions, a forgetting-supplementation component that maintains a productive balance between exploration and exploitation, and a dream-sharing component that promotes diversity among candidate solutions. Rigorous testing across realistic hospital environments confirms MO-DOA’s outstanding effectiveness, with results showing a 21.86% gain in resource utilization, a 30.95% decrease in patient waiting times, a 19.06% boost in patient satisfaction, and a 29.56% improvement in how evenly staff workloads are distributed. The algorithm’s emergency response capabilities are especially noteworthy, achieving bed assignments within 4.23 min and an equipment deployment success rate of 94.56%. Computationally, the algorithm proves highly efficient, with an average response time of 18.87 s and strong scalability across different operational scales. Collectively, these findings position MO-DOA as a powerful and practical tool for optimizing hospital operations in real time. Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

► Show Figures

Figure 1

17 pages, 749 KB

Open AccessArticle

Further Geometric Behavior of the Generalized Marcum Q-Function

by Khaled Mehrez, Abdulaziz Alenazi and Mohsan Raza

Symmetry 2026, 18(3), 467; https://doi.org/10.3390/sym18030467 - 9 Mar 2026

Viewed by 319

Abstract

In this paper, we investigate a class of analytic functions associated with the generalized Marcum Q-function and its Alexander transform. We establish sufficient conditions under which these functions exhibit important geometric properties in the open unit disk, including strong starlikeness, strong convexity, [...] Read more.

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

► Show Figures

Figure 1

17 pages, 307 KB

Open AccessArticle

Generalization of the Rafid Operator and Its Symmetric Role in Meromorphic Function Theory with Electrostatic Applications

by Aya F. Elkhatib, Atef F. Hashem, Adela O. Mostafa and Mohammed M. Tharwat

Symmetry 2025, 17(11), 1837; https://doi.org/10.3390/sym17111837 - 2 Nov 2025

Viewed by 468

Abstract

This study introduces a new integral operator

I_{p, μ}^{δ}

that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses:

Σ_{p}^{+} (δ, μ, α)

, consisting [...] Read more.

This study introduces a new integral operator

I_{p, μ}^{δ}

that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses:

Σ_{p}^{+} (δ, μ, α)

, consisting of functions with nonnegative coefficients, and

Σ_{p}^{+} (δ, μ, α, c)

, which further fixes the second positive coefficient. For these classes, we establish a necessary and sufficient coefficient condition, which serves as the foundation for deriving a set of sharp results. These include accurate coefficient bounds, distortion theorems for functions and derivatives, and radii of starlikeness and convexity of a specific order. Furthermore, we demonstrate the closure property of the class

Σ_{p}^{+} (δ, μ, α, c)

, identify its extreme points, and then construct a neighborhood theorem. All the findings presented in this paper are sharp. To demonstrate the practical utility of our symmetric operator paradigm, we apply it to a canonical fractional electrodynamics problem. We demonstrate how sharp distortion theorems establish rigorous, time-invariant upper bounds for a solitary electrostatic potential and its accompanying electric field, resulting in a mathematically guaranteed safety buffer against dielectric breakdown. This study develops a symmetric and consistent approach to investigating the geometric characteristics of meromorphic multivalent functions and their applications in physical models. Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

20 pages, 1668 KB

Open AccessArticle

Geometric Properties and Applications in System Modeling for a Generalized q-Symmetric Operator

by Abdelrahman M. Yehia, Atef F. Hashem, A. S. Al-Moisheer, Mohamed A. Sohaly, Samar M. Madian and Mohammed M. Tharwat

Symmetry 2025, 17(10), 1593; https://doi.org/10.3390/sym17101593 - 24 Sep 2025

Cited by 1 | Viewed by 687

Abstract

This paper introduces a novel generalized q-symmetric differential operator for studying a certain subclass of univalent functions with negative coefficients. We establish several significant theoretical results for this class, including sharp coefficient bounds and characterization theorems based on the generalized Hadamard product. Two significant applications demonstrate the theoretical framework’s practical utility. First, in the context of geometric modeling, we demonstrate how the function class and operator can be utilized to create and control complex, non-overlapping transformations. Second, in digital signal processing, we show that these functions serve as stable digital filter prototypes and that our operator is an effective tool for fine-tuning the filter’s frequency response. These applications bridge the gap between abstract geometric function theory and practical system design by demonstrating the operator’s versatility as a tool for analysis and synthesis. Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

► Show Figures

Journal Menu

Journal Browser

Symmetry in Complex Analysis Operators Theory

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (7 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI