Radii Of Starlikeness Research Articles

Certain Class of <i>P</i>-Valent Analytic Function Associated with Derivative Operator and Their Properties

This study aims to define a new subclass of multivalent analytic functions in the open unit disk. Jackson's derivative operator has been used to generate this subclass. Before getting coefficient characterization, we look at certain needs for the functions related to this subclass. We can see several fascinating features, including coefficient estimates, growth and distortion theorem, extreme points, and the radius of starlikeness and convexity of functions belonging to the subclass are shown using this technique.

Coefficient Bounds for q-Noshiro Starlike Functions in Conic Region

We present and examine a new family of analytic functions that can be described by a q-Ruscheweyh differential operator. We discuss several novel results, including coefficient inequalities and other noteworthy properties such as partial sums and radii of starlikeness. Moreover, coefficient estimates for the class of Janowski starlike functions associated with symmetric conic domains are also discussed.

Some Applications of Fractional Derivative Operator

Introduction: The aim of this paper is to introduce a new subclass of univalent functions with negative coefficients related to fractional derivative operator in the unit disk We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and close-to-convexity, extreme points, Hadamard product, and closure theorems for functions belonging to our class

ON A SPECIAL CLASS OF LOGHARMONIC MAPPINGS

This paper considers a special class SL(h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{L}(h)$$\\end{document} of logharmonic mappings of the form f(z)=h(z)h′(z)¯,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(z)=h(z)\\overline{h^{\\prime }(z)},$$\\end{document} where h is analytic in the unit disk U, normalized by h(0)=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h(0)=0$$\\end{document}, h′(0)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h^{\\prime }(0)=1$$\\end{document}, and h(U) is starlike. For this class of functions, a distortion theorem is proved, and Bohr’s inequality along with some improvements and refinements is investigated. In addition, the radius of starlikeness and an estimate for arclength are obtained.

Radius problems for certain classes of analytic functions

"Radius constants for functions in three classes of analytic functions to be a starlike function of order α, parabolic starlike function, starlike function associated with lemniscate of Bernoulli, exponential function, cardioid, sine function, lune, a particular rational function, and reverse lemniscate are obtained. One of these classes are characterized by the condition Re g/(zez ) > 0. The other two classes are defined by using the function g and they consist respectively of functions f satisfying Re f/g > 0 and |f/g − 1| < 1. Keywords: Starlike function, radius of starlikeness, exponential function."

SUBCLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH LINEAR OPERATOR

In this work, we introduce and study a new subclass of analytic functions defined by a linear operator and obtained coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are obtained. Furthermore, we obtained integral means inequalities for the class.

Certain Properties of Harmonic Functions Defined by a Second-Order Differential Inequality

The Theory of Complex Functions has been studied by many scientists and its application area has become a very wide subject. Harmonic functions play a crucial role in various fields of mathematics, physics, engineering, and other scientific disciplines. Of course, the main reason for maintaining this popularity is that it has an interdisciplinary field of application. This makes this subject important not only for those who work in pure mathematics, but also in fields with a deep-rooted history, such as engineering, physics, and software development. In this study, we will examine a subclass of Harmonic functions in the Theory of Geometric Functions. We will give some definitions necessary for this. Then, we will define a new subclass of complex-valued harmonic functions, and their coefficient relations, growth estimates, radius of univalency, radius of starlikeness and radius of convexity of this class are investigated. In addition, it is shown that this class is closed under convolution of its members.

A CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY KOMATU INTEGRAL OPERATOR

In this paper, we introduce a subclasses of analytic functions with negative coefficients defined by Komatu integral operator. We obtain the coefficient bounds, growth distortion properties, extreme points and radii of starlikeness and convexity and close-to-convexity for functions belonging to the class $TS_{a, \delta} ^{~ k} (\vartheta ,\hbar ,\ell )$. Furthermore, we obtained modified Hardamard product, closure properties for this class.

On Some Differential Operators Related to A Type of Meromorphic Univalent Functions

The goal of this article is to introduce a class of a type of meromorphic function which defined by some differential operators. Then we study various properties of these operators such as, coefficient inequality, both of growth and distortion theorems, radii of Star likeness and convexity of f(z) in the class that we present it.

On some geometric results for generalized k-Bessel functions

Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α \alpha -convexity. In addition, we show that the radii of α \alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , \alpha \in {[}0,1], and they are decreasing with respect to the parameter α . \alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.

Subclasses of p-Valent κ-Uniformly Convex and Starlike Functions Defined by the q-Derivative Operator

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator Sη,p,qn,m. Secondly, by means of this q-derivative operator, we define an interesting subclass Tℵλ,pn,m(η,α,κ) of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk U. This p-valent analytic function class is associated with the class κ-UCV of κ-uniformly convex functions and the class κ-UST of κ-uniformly starlike functions in U. For functions belonging to the normalized analytic and multivalent (or p-valent) function class Tℵλ,pn,m(η,α,κ), we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein.

Radius of starlikeness through subordination

"A normalized function $f$ on the open unit disc is starlike (or convex) univalent if the associated function $zf'(z)/f(z)$ (or $1+zf''(z)/f'(z)$) is a function with positive real part. The radius of starlikeness or convexity is usually obtained by using the estimates for functions with positive real part. Using subordination, we examine the radius of various starlikeness, in particular, radii of Janowski starlikeness and starlikeness of order $\beta$, for the function $f$ when the function $f$ is either convex or $(zf'(z)+\alpha z^2f''(z))/f(z)$ lies in the right-half plane. Radii of starlikeness associated with lemniscate of Bernoulli and exponential functions are also considered."

Starlike Functions Associated with Secant Hyperbolic Function

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbolic functions are discussed, which include the inclusion results, structural formula, certain sharp radii results such as radius of starlikeness and convexity of order α. It also finds a radius for ratios of analytic functions associated with Euler numbers.

Geometric Properties of Analytic Functions Defined by the (p, q) Derivative Operator Involving the Poisson Distribution

The objective of the current paper is to find the necessary and sufficient condition for the function to belong to the subclass of C d , δ , μ , β of analytic functions involving the Poisson distribution defined by the p , q derivative operator. Furthermore, distortion bounds, covering theorems, a radius of starlikeness, and convexity for functions belonging to this class are obtained.

CERTAIN SUBCLASSES OF MEROMORPHICALLY P-VALENT FUNCTIONS WITH POSITVE OR NEGATIVE COEFICIENTS USING DIFFERENTIAL OPERATOR

In this paper, we have introduced two subclasses and of meromorphically p-valent functions with positive and negative coefficients, defined by differential operator in the punctured unit disk and obtain some sharp results including coefficient inequality, distortion theorem, radii of starlikeness and convexity, closure theorems of these subclasses of meromorphically p-valent functions. We also derive some interesting results for the Hadamard products of functions belonging to the classes and .

Q -Janowski type close-to-convex functions associated with a convolution operator

In this paper, we will discuss some generalized sub-classes of analytic function related with close-to-convex functions in conic domains by using \(q\) -calculus. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of star likeness and growth and distortion for these classes. It is important to mention that our results are a generalization of several existing results.

Certain Subclasses of Meromorphic Functions Involving Differential Operator

We obtain the coefficient estimates, extreme points, distortion and growth boundaries, radii of starlikeness, convexity, and close-to-convexity, according to the main purpose of this paper.

Subclasses of Uniformly Convex Functions with Negative Coefficients Based on Deniz–Özkan Differential Operator

We introduce in this paper a new family of uniformly convex functions related to the Deniz–Özkan differential operator. By using this family of functions with a negative coefficient, we obtain coefficient estimates, the radius of starlikeness, convexity, and close-to-convexity, and we find their extreme points. Moreover, the neighborhood, partial sums, and integral means of functions for this new family are studied.

Some properties of differential operator to the subclass of univalent functions with negative coefficients

Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions is defined using a generalized differential operator and we have discussed a subclass \(TS_{\sigma, \delta} ^{~ \wp} (\vartheta ,\hbar ,\ell )\) of univalent functions with negative coefficients related to differential operator in the unit disk \( \mathbb { U }=\left \{{z \in \mathbb{ C }:|z|<1}\right \}\). We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and close-to-convexity, extreme points, Hadamard product, and closure theorems for functions belonging to our class.

New Subclass of K -Uniformly Univalent Analytic Functions with Negative Coefficients Defined by Multiplier Transformation

In this work, we shall derive a new subclass of univalent analytic functions denoted by H α , β , γ , k , λ , m in the open unit disk D = z ∈ ℂ : z &lt; 1 which is defined by multiplier transformation. Coefficient inequalities, growth and distortion theorem, extreme points, and radius of starlikeness and convexity of functions belonging to the subclass are obtained.