scholarly journals Some Properties of Certain Subclasses of Analytic Functions with Complex Order

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Zhi-Gang Wang ◽  
Feng-Hua Wen ◽  
Yong Sun
Keyword(s):  
Analytic Functions ◽  
Complex Order ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Coefficient Inequalities

The main purpose of this paper is to derive some coefficient inequalities and subordination properties for certain subclasses of analytic functions involving the Salagean operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

scholarly journals Certain Subordination Properties for Subclasses of Analytic Functions Involving Complex Order

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
S. Sivasubramanian ◽  
Aabed Mohammed ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Complex Order ◽  
Sălăgean Operator ◽  
Salagean Operator

We derive several subordination results for a certain class of analytic functions defined by the Sălăgean operator In the present investigation.

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

2017 ◽  
Vol 71 (1) ◽  
pp. 65
Author(s):  
A. Y. Lashin
Keyword(s):  
Complex Plane ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
General Class ◽  
Starlike Functions ◽  
Starlike And Convex Functions ◽  
Complex Order ◽  
Sălăgean Operator ◽  
Salagean Operator

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.

ON A SUBCLASS OF ANALYTIC FUNCTIONS WITH FIXED FINITELY MANY COEFFICIENTS BASED ON SALAGEAN OPERATOR AND MODIFIED SIGMOID FUNCTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2807-2820
Author(s):  
M.O. Oluwayemi ◽  
Olubunmi A. Fadipe Joseph ◽  
Sh. Najafzadeh
Keyword(s):  
Analytic Functions ◽  
Sigmoid Function ◽  
Geometric Properties ◽  
New Family ◽  
Sălăgean Operator ◽  
Salagean Operator

A new family of analytic functions involving sigmoid function defined as $ T_\gamma(\lambda, \beta, \alpha, \mu, c_m)\subset T_\gamma(\lambda, \beta, \alpha, \mu)$ are established. Certain geometric properties of the class are obtained.

Properties of the Salagean Operator

1998 ◽  
Vol 5 (4) ◽  
pp. 361-366
Author(s):  
Li Jian Lin ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sălăgean Operator ◽  
Salagean Operator

Abstract The object of the present paper is to show the properties of the Salagean operator for analytic functions in the open unit disk. The main results obtained here extend and improve the earlier results obtained by several authors.

scholarly journals Neighborhoods of certain classes of analytic functions with negative coefficients

2006 ◽  
Vol 2006 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Special Cases ◽  
Inclusion Relations

By making use of the familiar concept of neighborhoods of analytic functions, the author proves several inclusion relations associated with the(n,δ)-neighborhoods of various subclasses defined by Salagean operator. Special cases of some of these inclusion relations are shown to yield known results.

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

scholarly journals On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1305-1313
Author(s):  
Amol Patil ◽  
Uday Naik
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Coefficient Inequalities

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

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