Strong Starlikeness Research Articles

Geometric Properties and Hardy Spaces of Rabotnov Fractional Exponential Functions

The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order γ. Moreover, we find conditions so that the Rabotnov functions belong to the class of bounded analytic functions and Hardy spaces. Various consequences of these results are also presented.

New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators

In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize and improve several results, which appeared recently in the literature on the geometric function theory of complex analysis. We also prove some simple conditions for starlikeness, convexity, and the strong starlikeness of several one-parameter families of integral operators, including (for example) a certain μ-convex integral operator and the familiar Bernardi integral operator.

Starlikeness Associated with the Van Der Pol Numbers

In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order α, strong starlikeness, and some inclusion results. We also study radii problems for various classes of analytic functions. Furthermore, we investigate some coefficient-related problems which include the sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three.

Quasiconformal Extensions of Biharmonic Mappings and Strongly Starlike Biharmonic Mappings

Quasiconformal Extensions of Biharmonic Mappings and Strongly Starlike Biharmonic Mappings

On the Strong Starlikeness of the Bernardi Transform

Many papers concern both the starlikeness and the convexity of Bernardi integral operator. Using the Nunokawa’s Lemma, we want to determine conditions for the strong starlikeness of the Bernardi transform of normalized analytic functions g, such that |arg{g′(z)}| <απ2 in the open unit disk Δ where 0<α<2. Our results include the results of Mocanu, Nunokawa and others on the Libera transform.

Subordination Properties of Certain Operators Concerning Fractional Integral and Libera Integral Operator

The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying the Libera integral operator and fractional integral of order λ for analytic functions. Many subordination properties are obtained for this newly defined operator by using famous lemmas proved by important scientists concerned with geometric function theory, such as Eenigenburg, Hallenbeck, Miller, Mocanu, Nunokawa, Reade, Ruscheweyh and Suffridge. Results regarding strong starlikeness and convexity of order α are also discussed, and an example shows how the outcome of the research can be applied.

G−Loewner chain associated with Muir-type extension operator

In this paper, we will give two sufficient conditions that the Muir-type extension operator preserves the first element of a Loewner chain on the Reinhardt domain , where or . Using these conclusions, it can be easily proved that the Muir-type extension operator preserves starlikeness of order α and strong starlikeness.

Some geometric properties of certain families of q-Bessel functions

In this paper, we are mainly interested in finding sufficient conditions for the q-close-to-convexity of certain families of q-Bessel functions with respect to certain functions in the open unit disk. The strong convexity and strong star likeness of the same functions are also part of our investigation.

Harmonic spirallike functions and harmonic strongly starlike functions

In this note, we define two subclasses of normalized harmonic univalent functions of the unit disk, spirallike functions and strongly starlike functions, which preserve a hereditary property and have nice analytic and geometric characterizations. We also investigate the uniform boundedness and quasiconformal extendability of strongly starlike functions. Some coefficient conditions can be given for strong starlikeness and spirallikeness. We consider a special form of harmonic functions as an application.

Strongly Starlike Functions and Related Classes

We consider univalent functions, analytic in the unit disc $ |z|<1$in the complex plane ${\mathbb{C}}$ which map $ |z|<1$ onto a domainwith some nice property. The purpose of this paper is to find somenew conditions for strong starlikeness and some related results.

Sufficient Conditions for Strong Starlikeness

Let p be an analytic function defined on the open unit disc $$\mathbb {D}$$ with $$p(0)=1$$ and $$0< \alpha \le 1$$ . The conditions on complex valued functions C, D, and E are obtained for p to be subordinate to $$((1+z)/(1-z))^{\alpha }$$ when $$C(z) z^{2}p''(z)+D(z)zp'(z) + E(z)p(z)=0$$ . Sufficient conditions for confluent (Kummer) hypergeometric function and generalized and normalized Bessel function of the first kind of complex order to be subordinate to $$((1+z)/(1-z))^{\alpha }$$ are obtained as applications. The conditions on $$\alpha $$ and $$\beta $$ are derived for p to be subordinate to $$((1+z)/(1-z))^{\alpha }$$ when $$1+\beta zp'(z)/p^{n}(z)$$ with $$n=1,2$$ is subordinate to $$1+4z/3+2z^{2}/3=:\varphi _{CAR}(z)$$ . Similar problems were investigated for $${{\,\mathrm{Re}\,}}p(z)>0$$ when the function $$p(z)+\beta zp'(z)/p^{n}(z)$$ with $$n=0,2$$ is subordinate to $$\varphi _{CAR}(z)$$ . The condition on $$\beta $$ is determined for p to be subordinate to $$((1+z)/(1-z))^{\alpha }$$ when $$p(z)+\beta zp'(z)/p^{n}(z)$$ with $$n=0,1,2$$ is subordinate to $$((1+z)/(1-z))^{\alpha }$$ .

On strongly starlike and strongly convex functions with bounded radius and bounded boundary rotation

In this paper, we introduce and investigate new classes of normalized analytic functions in an open unit disk with bounded radius and bounded boundary rotation by using the subordination. We discuss inclusion results, co-efficient bounds, growth and distortion theorems of the classes. Moreover, we compute the radii of strong starlikeness, convexity and starlikeness of the classes. It is interesting to mention that most of our findings are best possible as compared to the existing results in the literature.

Criteria for a certain class of the Carath\xe9odory functions and their applications

In this paper, we obtain some potentially useful conditions (or criteria) for the Carathéodory functions as a certain class of analytic functions by applying Nunokawa’s lemma. We also obtain several conditions for strong starlikeness and close-to-convexity as special cases of the main results presented here.

Argument and Coefficient Estimates for Certain Analytic Functions

The aim of the present paper is to introduce a new class G α , δ of analytic functions in the open unit disk and to study some properties associated with strong starlikeness and close-to-convexity for the class G α , δ . We also consider sharp bounds of logarithmic coefficients and Fekete-Szegö functionals belonging to the class G α , δ . Moreover, we provide some topics related to the results reported here that are relevant to outcomes presented in earlier research.

On the order of strong starlikeness and the radii of starlikeness for of some close-to-convex functions

In this paper we show several sufficient conditions for close-to-convex functions to be strongly starlike of some order. The results continue the line of study from the first author’s paper on the order of strong starlikeness of strongly convex functions, (Nunokawa in Proc Japan Acad Ser A 69(7):234–237, 1993). Also it appears an small improvement of a certain classical results of Ch. Pommerenke. As an application, we also derive estimates for the radii of star-likeness for close-to-convex functions.

Radii problems for normalized q−Bessel and Wright functions

Abstract In this investigation, our main objective is to ascertain the radii of k-uniform convexity of order and the radii of strong starlikeness of the some normalized q-Bessel and Wright functions. In making this investigation we deal with the normalized Wright functions for three different kinds of normalization and six different normalized forms of q-Bessel functions. The key tools in the proof of our main results are the Mittag-Leffer expansion for Wright and q-Bessel functions and properties of real zeros of these functions and their derivatives. We also have shown that the obtained radii are the smallest positive roots of some functional equations.

A Certain Family of Integral Operators Associated with the Struve Functions

This article presents the study of Struve functions and certain integral operators associated with the Struve functions. It contains the investigation of certain geometric properties like the strong starlikeness and strong convexity of the Struve functions. It also includes the criteria of univalence for a family of certain integral operators associated with the generalized Struve functions. The starlikeness and uniform convexity of the said integral operators are also part of this research.

About strong starlikeness conditions

Some results concerning the strong starlikeness of analytic functions are improved. The techniques of convolutions are used.

Radii Problems for Normalized Bessel Functions of First Kind

For three different normalizations of Bessel functions of first kind, the radius of k-parabolic starlikeness and k-uniform convexity of order $$\alpha $$ are determined. The radius of strong starlikeness and other related radius are also obtained for these functions. We also find optimal parameters for which these functions are k-parabolic starlike and k-uniformly convex in the open unit disk.

Spirallikeness of shifted hypergeometric functions

In the present paper, we study spirallikenss (including starlikeness) of the shifted hypergeometric function $f(z)=z_2F_1(a,b;c;z)$ with complex parameters $a,b,c,$ where $_2F_1(a,b;c;z)$ stands for the Gaussian hypergeometric function. First, we observe the asymptotic behaviour of $_2F_1(a,b;c;z)$ around the point $z=1$ to obtain necessary conditions for $f$ to be $\lambda$-spirallike for a given $\lambda$ with $- \pi/2< \lambda<\pi/2.$ We next give sufficient conditions for $f$ to be $\lambda$-spirallike. As special cases, we obtain sufficient conditions of strong starlikeness and examples of spirallike, but not starlike, shifted hypergeometric functions.