398 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
Geometric Properties of Partial Sums of Univalent Functions
The th partial sum of an analytic function is the polynomial . A survey of the
univalence and other geometric properties of the th partial sum of univalent
functions as well as other related functions including those of starlike,
convex and close-to-convex functions are presented
Certain subclasses of multivalent functions defined by new multiplier transformations
In the present paper the new multiplier transformations
\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq
0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent
functions is defined. Making use of the operator two new subclasses and \textbf{\ }of multivalent analytic
functions are introduced and investigated in the open unit disk. Some
interesting relations and characteristics such as inclusion relationships,
neighborhoods, partial sums, some applications of fractional calculus and
quasi-convolution properties of functions belonging to each of these subclasses
and
are
investigated. Relevant connections of the definitions and results presented in
this paper with those obtained in several earlier works on the subject are also
pointed out
Ruscheweyh-Goyal Derivative of Fractional Order, its Properties Pertaining to Pre-starlike Type Functions and Applications
The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve the convexity and starlikeness for an analytic function. The majorization results for fractional Ruscheweyh-Goyal derivative has been discussed using a newly defined subclass
Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients I
For certain univalent function f, we study a class of functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying <CENTER>Re { (zJ<SUB>1</SUB><SUP>λ, μ</SUP> f(z))<SUP>'</SUP>)/((1 -γ) J<SUB>1</SUB><SUP>λ, μ</SUP> f(z) + γ z<SUP>2</SUP>(J<SUB>1</SUB><SUP>λ, μ</SUP> f(z))<SUP>"</SUP> )} > β.</CENTER> A necessary and sufficient condition for a function to be in the class A<SUB>γ</SUB><SUP>λ, μ, ν</SUP>(n, β) is obtained. In addition, our paper includes distortion theorem, radii of starlikeness, convexity and close-to-convexity, extreme points. Also, we get some results in this paper
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