scholarly journals On a Subclass of Analytic Functions That Are Starlike with Respect to a Boundary Point Involving Exponential Function

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Exponential Function ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Coefficient Estimates ◽  
New Class ◽  
Differential Subordinations ◽  
Class Of Functions

In the present exploration, the authors define and inspect a new class of functions that are regular in the unit disc D ≔ ς ∈ ℂ : ς < 1 , by using an adapted version of the interesting analytic formula offered by Robertson (unexploited) for starlike functions with respect to a boundary point by subordinating to an exponential function. Examples of some new subclasses are presented. Initial coefficient estimates are specified, and the familiar Fekete-Szegö inequality is obtained. Differential subordinations concerning these newly demarcated subclasses are also established.

scholarly journals On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

scholarly journals ON A CLASS OF MEROMORPHIC STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

1996 ◽  
Vol 27 (1) ◽  
pp. 15-26
Author(s):  
K. K. DIXIT ◽  
S. K. PAL
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Coefficient Estimates ◽  
Linear Combinations ◽  
Meromorphic Starlike Functions ◽  
Class Of Functions

Let $T^*_M(A, B, z_0)$ denote the class of functions \[f(z)=\frac{a}{z}-\sum_{n=1}^\infty a_nz^n, a\ge 1, a_n\ge 0\] regular and univalent in unit disc $U'=\{z:0<|z|<1\}$, satisfying the condition \[-z\frac{f'(z)}{f(z)}=\frac{1+Aw(z)}{1+Bw(z)}, \quad \text{ for } z\in U' \text{ and } w\in E\] (where $E$ is the class of analytic functions $w$ with $w(0) = 0$ and $|w(z)| \le 1$), where $-1\le A < B \le 1$, $0\le B \le 1$ and $f(z_0) =1/z_0$ ($0<z_0<1$). In this paper sharp coefficient estimates, distortion properties and radius of meromorphic convexity for functions in $T^*_M(A, B, z_0)$ have been obtained. We also study integral transforms of functions in $T^*_M(A, B, z_0)$. In the last, it is proved that the class $T^*_M(A, B, z_0)$ is closed under convex linear combinations.          

scholarly journals A new subclass of analytic functions defined by linear operator

2020 ◽  
pp. 205-217
Author(s):  
Santosh M. Popade ◽  
Rajkumar N. Ingle ◽  
P. Thirupathi Reddy ◽  
B. Venkateswarlu
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Partial Sums ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
New Class

In this work, we introduce and investigate a new class $ k- \widetilde{ U}S_s ( a, c , \gamma , t)$ of analytic functions in the open unit disc $U$ with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions $f$ belonging to this class.

scholarly journals Coefficient estimates for starlike functions

1977 ◽  
Vol 16 (3) ◽  
pp. 415-425 ◽  
Author(s):  
M.L. Mogra ◽  
O.P. Juneja
Keyword(s):  
Unit Disc ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Michigan Math ◽  
Image Position ◽  
Class Of Functions

Let (α β) denote the class of functionsanalytic in the unit disc Δ ≡{z: |z| < 1} and satisfyingfor some α, β (0 ≤ α < 1, 0 < β ≤ 1) and for all z ∈ Δ. In the present paper, sharp coefficient estimates for functions in (α, β) have been obtained. The results thus obtained not only generalize the corresponding results of Thomas H. MacGregor (Michigan Math. J. 10 (1963), 277–281), A.V. Boyd (Proc. Amer. Math. Soc. 17 (1966), 1016–1018) and others, but also give rise to analogous results for various other subclasses of starlike functions.

scholarly journals Some Properties for Certain Class of Analytic Functions with Varying Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa ◽  
A. Shamandy ◽  
E. A. Adwan
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
New Class ◽  
Salagean Operator ◽  
Distortion Theorems ◽  
Varying Arguments

We introduce a new class of analytic functions with varying arguments in the open unit disc defined by the Salagean operator. The object of the present paper is to determine coefficient estimates, extreme points, and distortion theorems for functions belonging to the class .

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

scholarly journals Coefficients estimates for functions inBn(α)

2003 ◽  
Vol 2003 (59) ◽  
pp. 3761-3767 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Differential Operator ◽  
Unit Disc ◽  
Coefficient Estimates ◽  
Class Of Functions

We consider functionsf, analytic in the unit disc and of the normalised formf(z)=z+∑k=2∞akzk. For functionsf∈Bn(α), the class of functions involving the Sălăgean differential operator, we give some coefficient estimates, namely,|a2|,|a3|, and|a4|.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

scholarly journals On a class of analytic functions

1975 ◽  
Vol 20 (1) ◽  
pp. 46-53
Author(s):  
R. M. Goel
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Image Position ◽  
Class Of Functions

Let S(α) denote the class of functions regular and analytic in the unit disc E = {z¦z¦< 1¦} and satisfying the condition, .

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