Functions Of Complex Order Research Articles

Coefficient bounds for the General Subclasses of Close-to-Convex Functions of Complex Order

Coefficient bounds for the General Subclasses of Close-to-Convex Functions of Complex Order

Estimating the Second Order Hankel Determinant for the Subclass of Bi-Close-to-Convex Function of Complex Order

The article aims to estimate the coefficient bounds for the second Hankel determinant by using the class of bi-close-to-convex functions of a complex order in the open unit disk. Making the direct application of Carathéodory function along with the closely related properties of starlike functions, we obtain the upper bound for the second Hankel determinant via certain subclass of bi-close-to-convex functions of complex order. The study discusses the maximization of the second Hankel determinant in both conventional graph and analytic methods. Moreover, we explore and modify some results on the study of bi-close-to-convex functions and its second degree Hankel determinant. At the end of the article, we remark on improvement in the earlier work of some researchers and discover a better value than the one they obtained.

Bazilevič Functions of Complex Order with Respect to Symmetric Points

In this paper, we familiarize a class of multivalent functions with respect to symmetric points related to the differential operator and discuss the impact of Janowski functions on conic regions. Inclusion results, the subordination property, and coefficient inequalities are obtained. Further, the applications of our results that are extensions of those given in earlier works are presented as corollaries.

Estimates for -spirallike function of complex order on the boundary

UDC 517.5 We give some results for -spirallike function of complex order at the boundary of the unit disc . The sharpness of these results is also proved. Furthermore, three examples for our results are considered.

Volterra-type operator on the subclasses of univalent functions

UDC 517.5 In this article, we examine the necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order and spirallike functions of type with the complex order We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions belonging to the mentioned classes. In the main part of this paper, we obtain the necessary and sufficient conditions of boundedness for the image of the open unit disk under the action of a Volterra-type operator and the product of the composition operator and Volterra-type operator in the space of univalent functions and its subspace. Finally, we obtain an estimate of the Schwartzian norm of the above operators in these spaces.

Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

Fekete-Szegö problem for generalized bi-subordinate functions of complex order

In this paper, we obtain the Fekete-Szegö inequality for the generalized bi-subordinate functions of complex order. The various results, which are presented in this paper, would generalize those in related works of several earlier authors.******************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

Fekete Szegö properties for a class of univalent functions of complex order associated with q-difference operator

In this paper we introduce new class of q-starlike and q-convex functions of complex order involving the q-derivative operator. Morever, we find estimates on the coefficients for functions in this class.

New subclasses bi-univalent functions related to shell-like curves involving hypergeometric functions

In the present paper, new subclasses of bi-univalent functions of complex order associated with hypergeometric functions are introduced and coefficient estimates for functions in these classes are obtained. Several new (or known) consequences of the results are also pointed out.

The Fekete–Szegö functional for generalized starlike and convex functions of complex order

New subclasses of analytic functions are defined by using the function [Formula: see text] given by the integral transform [Formula: see text]. Bounds for the Fekete–Szegö coefficient functional [Formula: see text] for these classes of functions are derived.

Subclass of Bazilevič functions of complex order

In this paper, we define a class of analytic functions by using the concept of complex order. This class of analytic functions generalizes the class of Bazilevic functions. In the present work, we derive various useful properties and characteristics of this class such as coefficient bounds, Fekete-Szego type inequality, arclength, integral preserving property, radius problem and some other interesting properties. Relevant connections of the results presented here with those obtained in earlier works are pointed.

Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order

In this paper, we obtain the upper bounds for the n-th (n ≥ 1) coefficients for meromorphic bi-subordinate functions of complex order by using Faber polynomial expansions. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

Ruscheweyh-type starlike functions of complex order associated with q-difference operator

In this paper, we introduce three new subclasses of starlike functions of complex order by using Ruscheweyh-type q-differential operator. We investigate inclusion theorem, sufficient coefficient estimates, distortion bounds and radius of starlikeness for the functions belonging to these subclasses. Moreover, partial sums of these subclasses were obtained.

Analytic Functions of Complex Order Defined by New Differential Operator

Analytic Functions of Complex Order Defined by New Differential Operator

Some subclasses of analytic functions of complex order

Some subclasses of analytic functions of complex order

Coefficients estimates for certain classes of analytic functions of complex order

In this paper, we introduce and investigate the subclasses $$\mathcal {Q} _{g}^{\zeta }(m,\lambda ,\mu ;\gamma )$$ and $$\mathcal {H}_{g}^{\zeta }(m,\lambda ,\mu ,r;u)$$ of analytic functions of complex order defined by a new differential operator involving binomial series. Furthermore, We obtain coefficients bounds and coefficient estimates involving of the nonhomogeneous Cauchy–Euler differential equation of order r. Several corollaries of the main results are also considered.

Subclasses of Analytic Functions of Complex Order Involving Jackson’s (p, q)-derivative

In this paper, we introduce a new differential operator defined by the Jackson’s (p, q)-derivative. Making use of this differential operator, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. For this subclass, we obtain coefficient estimates, extreme points, and integral means inequalities. Furthermore, we obtain some distortion theorems involving fractional integrals and fractional derivatives. Several special cases of our results are also pointed out.

Subclasses of Multivalent Functions of Complex Order Related to Sigmoid Function

Subclasses of Multivalent Functions of Complex Order Related to Sigmoid Function

On a Generalization of Bounded Univalent Function of Complex Order

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.

Convolution conditions for bounded \(\alpha\)-starlike functions of complex order

Let \(A\) be the class of analytic functions in the unit disc \(U\) of the complex plane \(\mathbb{C}\) with the normalization \(f(0)=f^{^{\prime }}(0)-1=0\). We introduce a subclass \(S_{M}^{\ast }(\alpha ,b)\) of \(A\), which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class \(S_{M}^{\ast }(n,\alpha ,b)\) (\(n\geq 0\)) related to \(S_{M}^{\ast }(\alpha ,b)\) is also considered under the same conditions. Among other things, we find convolution conditions for a function \(f\in A\) to belong to the class \(S_{M}^{\ast }(\alpha ,b)\). Several properties of the class \(S_{M}^{\ast }(n,\alpha ,b)\) are investigated.