The Ruscheweyh derivative operator is used in this paper to introduce and
investigate interesting general subclasses of the function class
Σm of m-fold symmetric bi-univalent analytic functions.
Estimates of the initial Taylor-Maclaurin coefficients ∣am+1∣
and ∣a2m+1∣ are obtained for functions of the subclasses
introduced in this study, and the consequences of the results are discussed.
The results presented would generalize and improve on some recent works by many
earlier authors. In some cases, our estimates are better than the existing
coefficient bounds. Furthermore, within the engineering domain, this paper
delves into a series of complex issues related to analytic functions, m-fold
symmetric univalent functions, and the utilization of the Ruscheweyh derivative
operator. These problems encompass a broad spectrum of engineering
applications, including the optimization of optical system designs, signal
processing for antenna arrays, image compression techniques, and filter design
for control systems. The paper underscores the crucial role of these
mathematical concepts in addressing practical engineering dilemmas and
fine-tuning the performance of various engineering systems. It emphasizes the
potential for innovative solutions that can significantly enhance the
reliability and effectiveness of engineering applications.Comment: 15 page