4 research outputs found
Some -Fold Symmetric Bi-Univalent Function Classes and Their Associated Taylor-Maclaurin Coefficient Bounds
The Ruscheweyh derivative operator is used in this paper to introduce and
investigate interesting general subclasses of the function class
of -fold symmetric bi-univalent analytic functions.
Estimates of the initial Taylor-Maclaurin coefficients
and 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, -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
A comprehensive subclass of bi-univalent functions defined by a linear combination and satisfying subordination conditions
In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained
Hankel determinant for a general subclass of m-fold symmetric biunivalent functions defined by Ruscheweyh operators
Abstract Making use of the Hankel determinant and the Ruscheweyh derivative, in this work, we consider a general subclass of m-fold symmetric normalized biunivalent functions defined in the open unit disk. Moreover, we investigate the bounds for the second Hankel determinant of this class and some consequences of the results are presented. In addition, to demonstrate the accuracy on some functions and conditions, most general programs are written in Python V.3.8.8 (2021)
Hankel determinant for a general subclass of m-fold symmetric bi-univalent functions defined by Ruscheweyh operator
Making use of the Hankel determinant and the Ruscheweyh derivative, in this
work, we consider a general subclass of m-fold symmetric normalized
bi-univalent functions defined in the open unit disk. Moreover, we investigate
the bounds for the second Hankel determinant of this class and some
consequences of the results are presented. In addition, to demonstrate the
accuracy on some functions and conditions, most general programs are written in
Python V.3.8.8 (2021).Comment: 16 pages, 7 figure