Briot-Bouquet Differential Subordination Research Articles

Results for Analytic Function Associated with Briot–Bouquet Differential Subordinations and Linear Fractional Integral Operators

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems.

P-VALENTLY BAZILEVIˇ C FUNCTIONS DEFINED WITH HIGHER ORDER DERIVATIVES

The object of this paper is to derive various properties and characters for a class of p-valently Bazileviˇ c functions defined with higher order derivatives. Using the technique of Briot-Bouquet differential subordination we obtained several results, some of them presented here generalize and improve a few earlier results, and several others are new ones involving differential inequalities. These last implications deal with the symmetric open disc and symmetric conic domains with respect to the real axe. Our results extends and improves many other previous ones, and some of them are the best possible under the given assumptions.

Briot–Bouquet Subordination Properties for Analytic Functions Involving Choi–Saigo–Srivastava Integral Operator

We consider a new subclass of starlike functions involving the Choi–Saigo–Srivastava integral operator associated with the sine function in open unit disc. In view of this function class, we examine majorization properties and Briot–Bouquet differential subordination relations for such functions.

Logarithmic Coefficients Inequality for the Family of Functions Convex in One Direction

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modulus of these coefficients has received attention. In this research, we obtain sharp bounds of the inequality involving the logarithmic coefficients for the functions of the well-known class G and investigate a majorization problem for the functions belonging to this family. To prove our main results, we use the Briot–Bouquet differential subordination obtained by J.A. Antonino and S.S. Miller and the result of T.J. Suffridge connected to the Alexander integral. Combining these results, we give sharp inequalities for two types of sums involving the modules of the logarithmical coefficients of the functions of the class G indicating also the extremal function. In addition, we prove an inequality for the modulus of the derivative of two majorized functions of the class G, followed by an application.

A new inner approach for differential subordinations

In this paper we introduce and examine the differential subordination of the form \[ p(z)+zp'(z)\varphi(p(z),zp'(z))\prec h(z),\quad z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}, \]where $h$ is a convex univalent function with $0\in h(\mathbb {D}).$ The proof of the main result is based on the original lemma for convex univalent functions and offers a new approach in the theory. In particular, the above differential subordination leads to generalizations of the well-known Briot-Bouquet differential subordination. Appropriate applications among others related to the differential subordination of harmonic mean are demonstrated. Related problems concerning differential equations are indicated.

Briot–Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function

We define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot–Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot–Bouquet differential equations and observe that these solutions are the best dominant of the Briot–Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions.

Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator

In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions.

On Certain Differential Subordination of Harmonic Mean Related to a Linear Function

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

Applications of Briot-Bouquet differential subordination

Applications of Briot-Bouquet differential subordination

Sufficient conditions for univalence obtained by using Briot-Bouquet differential subordination

In this paper, we define the operator Im : differential-integral operator, where Sm is S˘al˘agean differential operator and Lm is Libera integral operator. By using the operator Im the class of univalent functions denoted by is defined and several differential subordinations are studied. Even if the use of linear operators and introduction of new classes of functions where subordinations are studied is a well-known process, the results are new and could be of interest for young researchers because of the new approach derived from mixing a differential operator and an integral one. By using this differential–integral operator, we have obtained new sufficient conditions for the functions from some classes to be univalent. For the newly introduced class of functions, we show that is it a class of convex functions and we prove some inclusion relations depending on the parameters of the class. Also, we show that this class has as subclass the class of functions with bounded rotation, a class studied earlier by many authors cited in the paper. Using the method of the subordination chains, some differential subordinations in their special Briot-Bouquet form are obtained regarding the differential–integral operator introduced in the paper. The best dominant of the Briot-Bouquet differential subordination is also given. As a consequence, sufficient conditions for univalence are stated in two criteria. An example is also illustrated, showing how the operator is used in obtaining Briot–Bouquet differential subordinations and the best dominant.

Coefficient bounds for a new class of univalent functions involving Salagean operator and the modified Sigmoid function

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

On some differential subordinations

The purpose of this work is to present a new geometric approach to some problems in differential subordination theory. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

Some applications of first-order differential subordinations

Abstract In this work we present a new geometric approach to some problems in differential subordination theory. In the paper some sufficient conditions for function to be starlike or univalent or to be in the class of Carathéodory functions are obtained. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

An extension of Briot–Bouquet differential subordinations with an application to Alexander integral transforms

This article studies extensions of the well-known Briot–Bouquet differential subordination resultWe extend the result by determining conditions on the functions and so thatThis extension is used to prove several new results about Alexander transforms of spiral-like functions, including a conjecture of Kim and Srivastava.

On differential subordinations in the complex plane

The purpose of this work is to present a new approach to solve some problems in differential subordination theory. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

Applications of Multivalent Functions Associated with Generalized Fractional Integral Operator

By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator which was defined by Owa, Saigo and Srivastava [1]. Some interesting further consequences are also considered.

The exact order of starlikeness of uniformly convex functions

A Briot–Bouquet differential subordination is used to determine the exact order of starlikeness for the class of uniformly convex functions. In the solution we use some integral representations, which offer the possibility of correct estimation.

Subordination properties of certain classes of multivalently analytic functions

By using a method based upon the principle of the Briot–Bouquet differential subordination, we obtain a sharp result for p -valently starlikeness of certain normalized and multivalently analytic functions. Our investigation of such families of multivalently analytic functions is motivated essentially by a recent study by Nunokawa et al. [M. Nunokawa, S. Owa, T. Sekine, R. Yamakawa, H. Saitoh and J. Nishiwaki, On certain multivalent functions, Internat. J. Math. Math. Sci. 2007 (2007) 1–5. Article ID 72393]. We also give an answer to the open problem which was posed in the aforementioned article by Nunokawa et al.

On a differential subordination of some certain subclass of Univalent function

We generate some results for some particular subclasses of starlike and close-to-convex functions using Briot-Bouquet differential subordination method. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 181-184

On a class of analytic multivalent functions

We use a property of the Bernardi operator in the theory of the Briot–Bouquet differential subordinations to prove several theorems for the classes V k p ( H ; A , B ) of multivalent analytic functions defined by using the Dziok–Srivastava operator H . Some of these results we obtain applying the convolution property due to Rusheweyh. We take advantage of the Miller–Mocanu lemma to improve the earlier result.