Mathematics

Journal Browser

► Journal Browser

New Trends in Polynomials and Mathematical Analysis

Share This Special Issue

Special Issue Editor

Dr. Mohamed Illafe

E-Mail Website
Guest Editor

School of Engineering, Math, & Technology, Navajo Technical University, Crownpoint, NM 87313, USA
Interests: geometric function theory; analytic functions; special functions; fractional calculus; calculus; their applications in fluid mechanics, mathematical physics, control theory, and signal and image processing

Special Issue Information

Dear Colleagues,

Polynomials and their generalizations continue to play a vital role in modern mathematical analysis, with applications spanning operator theory, complex analysis, and fractional calculus. Among these areas, geometric function theory (GFT) offers a rich framework for studying the analytic and geometric properties of complex valued functions, especially when characterized by special polynomials and transformation operators.

Recent trends in this domain include the use of orthogonal polynomials, fractional and qqq-calculus, and generalized operators in the definition and classification of various function classes. These tools have also led to new results in coefficient problems, Hankel determinants, subordination principles, and functional inequalities. Beyond theoretical interest, such advances find applications in mathematical physics, signal processing, control theory, and dynamical systems.

This Special Issue invites original research articles related to the following:

Polynomial-based analytic function classes;
Univalent and bi-univalent functions;
Differential subordination and superordination;
Operators involving special functions and polynomials;
Fractional and qqq-calculus in function theory;
Applications of polynomial methods in mathematical modeling.

We welcome contributions that explore both theoretical developments and practical applications, aiming to capture the evolving landscape of mathematical analysis shaped by polynomial structures and new analytical tools.

We look forward to your valuable submissions.

Dr. Mohamed Illafe
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.

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 (2 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

16 pages, 315 KB

Open AccessArticle

Applications of Bernoulli Polynomials and q²-Srivastava–Attiya Operator in the Study of Bi-Univalent Function Classes

by Basem Aref Frasin, Sondekola Rudra Swamy, Ibtisam Aldawish and Paduvalapattana Kempegowda Mamatha

Mathematics 2025, 13(21), 3384; https://doi.org/10.3390/math13213384 - 24 Oct 2025

Viewed by 85

Abstract

The central focus of this study is the development and investigation of a generalized subclass of bi-univalent functions, defined using the

q^{2}

-Srivastava–Attiya operator in conjunction with Bernoulli polynomials. We derive initial coefficient estimates for functions in the newly proposed class and [...] Read more.

The central focus of this study is the development and investigation of a generalized subclass of bi-univalent functions, defined using the

q^{2}

-Srivastava–Attiya operator in conjunction with Bernoulli polynomials. We derive initial coefficient estimates for functions in the newly proposed class and also provide bounds for the Fekete–Szegö functional. In addition to presenting several new findings, we also explore meaningful connections with previously established results in the theory of bi-univalent and subordinate functions, thereby extending and unifying the existing literature in a novel direction. Full article

(This article belongs to the Special Issue New Trends in Polynomials and Mathematical Analysis)

15 pages, 851 KB

Open AccessArticle

Third-Order Hankel Determinant for a Class of Bi-Univalent Functions Associated with Sine Function

by Mohammad El-Ityan, Mustafa A. Sabri, Suha Hammad, Basem Frasin, Tariq Al-Hawary and Feras Yousef

Mathematics 2025, 13(17), 2887; https://doi.org/10.3390/math13172887 - 6 Sep 2025

Cited by 1 | Viewed by 514

Abstract

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to

1 + s i n z

. Coefficient bounds are obtained for the initial Taylor–Maclaurin coefficients, with a [...] Read more.

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to

1 + s i n z

. Coefficient bounds are obtained for the initial Taylor–Maclaurin coefficients, with a particular focus on the second- and third-order Hankel determinants. To illustrate the non-emptiness of the proposed class, we consider the function

\sqrt{1 + tanh z}

, which maps the unit disk onto a bean-shaped domain. This function satisfies the required subordination condition and hence serves as an explicit member of the class. A graphical depiction of the image domain is provided to highlight its geometric characteristics. The results obtained in this work confirm that the class under study is non-trivial and possesses rich geometric structure, making it suitable for further development in the theory of geometric function classes and coefficient estimation problems. Full article

(This article belongs to the Special Issue New Trends in Polynomials and Mathematical Analysis)

► Show Figures

Journal Menu

Journal Browser

New Trends in Polynomials and Mathematical Analysis

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (2 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI