Radii Of Starlikeness Research Articles

Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag–Leffler Functions

Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag–Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p,q)-variations.

A New Class of Holomorphic Univalent Functions Defined by Linear Operator

In the present work, we submit and study a new class AN(τ, λ, η, ρ) containing holomorphic univalent functions defined by linear operator in the open unit disk Λ={s ϵ C :|s | <1} We get some geometric properties, such as, coefficient inequality, growth, and distortion bounds, convolution properties, convex set, neighborhood property, radii of starlikeness and convexity , weighted mean and arithmetic mean for functions belonging to the class AN(τ, λ, η, ρ)

Some Geometrical Results Associated with Secant Hyperbolic Functions

In this paper, we examine the differential subordination implication related with the Janowski and secant hyperbolic functions. Furthermore, we explore a few results, for example, the necessary and sufficient condition in light of the convolution concept, growth and distortion bounds, radii of starlikeness and partial sums related to the class Ssech∗.

A Certain Subclass of Multivalent Functions Associated with Borel Distribution Series

In this paper, we determine the necessary and sufficient conditions for the power series f(z) whose coefficients are probabilities of the Borel distribution to be in the family J(p,λ ,α,β,γ) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.

New Class of Multivalent Functions with Negative Coefficients

In the present paper, we define a new class NA(n,p,λ,α,β) of multivalent functions which are holomorphic in the unit disk ∆ ={s∈C∶|s|<1}. A necessary and sufficient condition for functions to be in the class NA(n,p,λ,α,β) is obtained. Also, we get some geometric properties like radii of starlikeness, convexity and close-to-convexity, closure theorems, extreme points, integral means inequalities and integral operators.

On a subclass of meromorphic functions with positive coefficients defined by rapid operator

In this paper, we introduce and study a new subclass of meromorphic univalent functions defined by Rapid operator. We obtain coefficient inequalities, extreme points, radius of starlikeness and convexity. Finally we obtain partial sums and neighborhood properties for the class ∑*p(γ,κ,μ,θ)

A Generalized Subclass of p-VALENT Analytic Functions

Abstract: In this paper, a class ( , , , ) , k  p     of functions F analytic in the unit disk U={z:|z|<1} of the form        t n p t p t p F(z) z a z , (p, n N,  0 pt a for t  n) is considered. Coefficient inequality, distortion theorem, extreme points, starlikeness and convexity for this class are obtained. Keywords: Analytic functions, p-valent functions, extreme points, radii of starlikeness and convexity. 2010 AMS Subject classification: Primary 30C45.

Properties of q-Starlike Functions Associated with the q-Cosine Function

In this paper, our main focus is to define a new subfamily of q-analogue of analytic functions associated with the q-cosine function. Furthermore, we investigate some useful results such as the necessary and sufficient condition based on the convolution idea, growth and distortion bounds, closure theorem, convex combination, radii of starlikeness, extreme point theorem and partial sums results for the newly-defined functions class.

On a Certain Subclass of Analytic Functions Defined by Touchard Polynomials

This paper focuses on the establishment of a new subfamily of analytic functions including Touchard polynomials. Then, we attempt to obtain geometric properties such as coefficient inequalities, distortion properties, extreme points, radii of starlikeness and convexity, partial sums, neighbourhood results and integral means’ inequality for this class. The symmetry properties of the subfamily of functions established in the current paper may be examined as future research directions.

Radii of Starlikeness and Convexity of the Derivatives of Bessel Function

Radii of Starlikeness and Convexity of the Derivatives of Bessel Function

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

The Atangana–Baleanu fractional integral and multiplier transformations are two functions successfully used separately in many recently published studies. They were previously combined and the resulting function was applied for obtaining interesting new results concerning the theories of differential subordination and fuzzy differential subordination. In the present investigation, a new approach is taken by using the operator previously introduced by applying the Atangana–Baleanu fractional integral to a multiplier transformation for introducing a new subclass of analytic functions. Using the methods familiar to geometric function theory, certain geometrical properties of the newly introduced class are obtained such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity, and close-to-convexity of functions belonging to the class. This class may have symmetric or assymetric properties. The results could prove interesting for future studies due to the new applications of the operator and because the univalence properties of the new subclass of functions could inspire further investigations having it as the main focus.

Applications of the Atangana–Baleanu Fractional Integral Operator

Applications of the Atangana–Baleanu fractional integral were considered in recent studies related to geometric function theory to obtain interesting differential subordinations. Additionally, the multiplier transformation was used in many studies, providing elegant results. In this paper, a new operator is defined by combining those two prolific functions. The newly defined operator is applied for introducing a new subclass of analytic functions, which is investigated concerning certain properties, such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and radii of starlikeness, convexity and close-to-convexity. This class may have symmetric or asymmetric properties. The results could prove interesting due to the new applications of the Atangana–Baleanu fractional integral and of the multiplier transformation. Additionally, the univalence properties of the new subclass of functions could inspire researchers to conduct further investigations related to this newly defined class.

Certain class of multivalent functions with linear operator

This paper presents a certain class of analytic and multivalent functions with linear operator defined on unit. We obtained many geometric properties like, Coefficient’s inequality, Distortion and Growth theorem, Radii of starlikeness and Neighborhood.

A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator

Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results.

Some properties of analytical functions related to Borel distribution series

In this paper, we introduce and study a new subclass of analytic functions which are defined by means of a linear operator. Some results connected to coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity close-to-convexity and integral means inequalities related to the subclass is obtained.

Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship between the results and some known results in literature are also established.

$ q $-Noor integral operator associated with starlike functions and $ q $-conic domains

<abstract><p>In this paper, we will discuss some generalized classes of analytic functions related with conic domains in the context of $ q $-calculus. In this work, we define and explore Janowski type $ q $-starlike functions in $ q $ -conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness, growth and distortion results for these classes. It is important to mention that our results are generalization of number of existing results.</p></abstract>

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

Abstract In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class T S λ m ( γ , e , k , v ) TS_\lambda ^m(\gamma ,e,k,v) . Furthermore, we obtained the Fekete-Szego problem for this class.

New Subclass of Meromorphic Functions Associated with Hypergeometric Function

In this paper, we determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions The hypergeometric meromorphic functions have certain formula in the punctured unit disk which contains in new subclass.

Radii of starlikeness and convexity of Bessel function derivatives

UDC 517.5 In this paper, our aim is to find the radii of starlikeness andconvexity of Bessel function derivatives for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for th derivative of Bessel function andproperties of real zeros of it. In addition, by using the Euler–Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized th derivative of Bessel function. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind.