scholarly journals On the generalised Ruscheweyh class of analytic functions of complex order

1993 ◽  
Vol 47 (2) ◽  
pp. 247-257 ◽  
Author(s):  
O.P. Ahuja
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Order Complex ◽  
Sharp Estimates ◽  
Complex Order ◽  
Special Cases ◽  
The Family ◽  
Uniform Treatment

The main object of this paper is to identify various classes of analytic functions which are starlike, convex, pre-starlike, Ruscheweyh class of order α, β-spiral-like, β-convex-spiral-like, starlike of complex order, complex of complex order, and others as special cases of a family of analytic functions of complex order in the unit disk. This makes a uniform treatment possible. Finally, we derive sharp estimates for all coefficients of the functions from the family.

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

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

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.

scholarly journals Geometric Properties of a New Integral Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases.

scholarly journals Certain Subclass of Analytic Functions Defined by Wanas Operator

2021 ◽  
pp. 137-144
Author(s):  
Timilehin Gideon Shaba ◽  
Abbas Kareem Wanas ◽  
Ismaila Omeiza Ibrahim
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

In present article, we introduce and study a certain family of analytic functions defined by Wanas operator in the open unit disk. We establish some important geometric properties for this family. Further we point out certain special cases for our results.

"ESSENTIAL PROBLEMS FOR SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED ON UNIT DISK "

2021 ◽  
Vol 8 (1) ◽  
pp. 67-73
Author(s):  
Kassim A. Jassim
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Special Cases

"In this paper, we investigate subordinate problems for subclass related to known functions convoluted with Frasin operator. Therefore, major results and special cases are obtained.

scholarly journals Sharp estimates of generalized zalcman functional of early coeffcients for Ma-Minda type functions

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6267-6280 ◽  
Author(s):  
Nak Cho ◽  
Oh Kwon ◽  
Adam Lecko ◽  
Young Sim
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sharp Bounds ◽  
Sharp Estimates

Let ? be an analytic function in the unit disk D := {z ? C : |z| < 1} which has the form ?(z) = 1 + p1z + p2z2 + p3z3 + ... with p1 > 0, p2, p3 ? R. For given such ?, let S*(?), K(?) and R(?) denote the classes of standardly normalized analytic functions f in D which satisfy zf'(z)/f(z) < ?(z), 1 + zf''(z)/f'(z) < ?(z) f'(z)< ?(z), z ? D, respectively, where < means the usual subordination. In this paper, we find the sharp bounds of |a2a3-a4|, where an := f(n)(0)/n!; n ? N, over classes S*(?), K(?) and R(?).

scholarly journals ANGULAR ESTIMATIONS OF CERTAIN ANALYTIC FUNCTIONS

1998 ◽  
Vol 29 (1) ◽  
pp. 47-53
Author(s):  
NAK EUN CHO ◽  
IN HWA KIM
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

The object of the present paper is to investigate some argument properties of certain analytic functions in the open unit disk. Our resuIt contain some interesting corollaries as the special cases.

scholarly journals On the Fekete-Szegö Problem for a Class of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zhigang Peng
Keyword(s):  
Power Series ◽  
Real Number ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Upper Bounds ◽  
The Family ◽  
Class Of Functions

Let 𝒜 denote the class of functions which are analytic in the unit disk D={z:|z|<1} and given by the power series f(z)=z+∑n=2∞‍anzn. Let C be the class of convex functions. In this paper, we give the upper bounds of |a3-μa22| for all real number μ and for any f(z) in the family 𝒱={f(z):f∈𝒜, Re(f(z)/g(z))>0 for  some g∈C}.

scholarly journals Subordination by convex functions

2006 ◽  
Vol 2006 ◽  
pp. 1-6 ◽  
Author(s):  
Rosihan M. Ali ◽  
V. Ravichandran ◽  
N. Seenivasagan
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Subordination Result ◽  
Special Cases

For a fixed analytic functiong(z)=z+∑n=2∞gnzndefined on the open unit disk andγ<1, letTg(γ)denote the class of all analytic functionsf(z)=z+∑n=2∞anznsatisfying∑n=2∞|angn|≤1−γ. For functions inTg(γ), a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.

scholarly journals Certain Class of Analytic Functions with respect to Symmetric Points Defined by Q-Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
K. R. Karthikeyan ◽  
G. Murugusundaramoorthy ◽  
S. D. Purohit ◽  
D. L. Suthar
Keyword(s):  
Integral Representation ◽  
Representation Theorem ◽  
Analytic Functions ◽  
Type Star ◽  
Coefficient Bounds ◽  
Quantum Calculus ◽  
Complex Order ◽  
Special Cases ◽  
Symmetric Points

In this study, we familiarise a novel class of Janowski-type star-like functions of complex order with regard to j , k -symmetric points based on quantum calculus by subordinating with pedal-shaped regions. We found integral representation theorem and conditions for starlikeness. Furthermore, with regard to j , k -symmetric points, we successfully obtained the coefficient bounds for functions in the newly specified class. We also quantified few applications as special cases which are new (or known).

scholarly journals Некоторые результаты о подчинении для одного функционального класса, определяемого $q$-разностным оператором типа Салагина

2020 ◽  
pp. 7-15
Author(s):  
M.K. Aouf ◽  
T.M. Seoudy
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Mathematical Science ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Quantum Calculus ◽  
Complex Order ◽  
Principle Of Subordination

The theory of the basic quantum calculus (that is, the basic q-calculus) plays important roles in many diverse areas of the engineering, physical and mathematical science. Making use of the basic definitions and concept details of the q-calculus, Govindaraj and Sivasubramanian [10] defined the Salagean type q-difference (q-derivative) operator. In this paper, we introduce a certain subclass of analytic functions with complex order in the open unit disk by applying the Salagean type q-derivative operator in conjunction with the familiar principle of subordination between analytic functions. Also, we derive some geometric properties such as sufficient condition and several subordination results for functions belonging to this subclass. The results presented here would provide extensions of those given in earlier works.

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