New Trends in Polynomials and Mathematical Analysis

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

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