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 On generalized spiral-like analytic functions

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1493-1503 ◽  
Author(s):  
Khalida Noor ◽  
Nazar Khan ◽  
Muhammad Noor
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disc ◽  
New Class ◽  
Bounded Radius Rotation ◽  
Number Of Classes ◽  
Inclusion Results

In this paper, we use the concept of bounded Mocanu variation to introduce a new class of analytic functions, defined in the open unit disc, which unifies a number of classes previously studied such as those of functions with bounded radius rotation and bounded Mocanu variation. It also generalizes the concept of ?-spiral likeness in some sense. Some interesting properties of this class including inclusion results, arclength problems and a sufficient condition for univalency are studied.

scholarly journals A CONVOLUTION APPROACH TO CERTAIN SUBCLASSES OF STARLIKE FUNCTIONS

1992 ◽  
Vol 23 (4) ◽  
pp. 311-320
Author(s):  
T . RAM REDDY ◽  
O. P. JUNEJA ◽  
K. SATHYANARAYANA
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disc ◽  
Containment Property ◽  
Convolution Approach

The class $R_\gamma(A,B)$ for $-1\le B < A\le 1$ and $\gamma> (A- 1)/(1- B)$ consisting of normalised analytic functions in the open unit disc is defined with the help of Convolution technique. It consists of univalent starlike functions for $\gamma\ge 0$. We establish containment property, integral transforms and a sufficient condition for an analytic function to be in $R\gamma(A,B)$. Using the concept of dual spaces we find a convolution condition for a function in this class.

scholarly journals Coefficient estimate for a subclass of close-to-convex functionswith respect to symmetric points

2011 ◽  
Vol 42 (2) ◽  
pp. 217-222
Author(s):  
B. S. Mehrok ◽  
Gagandeep Singh ◽  
Deepak Gupta
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Symmetric Points

For reals $A,B,C,D$  such that  $-1\le D \le  B< A\le  C\le 1$, a subclass $K_s(A,B;C,D)$ of analytic functions $f(z)=z+\sum_{k=2}^\infty a_kz^k $ in the open unit disc $E=\{z:|z|<1\} $ is introduced. The object of the present paper is todetermine the coefficient estimate for functions $f(z)$ belonging tothe class  $K_s(A,B;C,D)$.

scholarly journals Starlikeness of Analytic Functions with Subordinate Ratios

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Rosihan M. Ali ◽  
Vaithiyanathan Ravichandran ◽  
Kanika Sharma
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Radius Of Starlikeness

Let h be a nonvanishing analytic function in the open unit disc with h 0 = 1 . Consider the class consisting of normalized analytic functions f whose ratios f z / g z , g z / z p z , and p z are each subordinate to h for some analytic functions g and p . The radius of starlikeness of order α is obtained for this class when h is chosen to be either h z = 1 + z or h z = e z . Further, starlikeness radii are also obtained for each of these two classes, which include the radius of Janowski starlikeness, and the radius of parabolic starlikeness.

Generalized q-starlike functions

2017 ◽  
Vol 54 (4) ◽  
pp. 509-522 ◽  
Author(s):  
Khalida Inayat Noor ◽  
Sadia Riaz
Keyword(s):  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Distortion Theorems ◽  
Bounded Radius Rotation ◽  
Radius Problem

In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

scholarly journals Second Hankel Determinants for Some Subclasses of Biunivalent Functions Associated with Pseudo-Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
K. Rajya Laxmi ◽  
R. Bharavi Sharma
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Starlike Function ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Hankel Determinants ◽  
Second Hankel Determinant ◽  
Starlike Univalent Function

We introduce second Hankel determinant of biunivalent analytic functions associated with λ-pseudo-starlike function in the open unit disc Δ subordinate to a starlike univalent function whose range is symmetric with respect to the real axis.

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.

Coefficient Inequalities for Lp-Valued Analytic Functions

1981 ◽  
Vol 24 (3) ◽  
pp. 347-350
Author(s):  
Lawrence A. Harris
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Inequalities

AbstractA Hausdorff-Young theorem is given for Lp-valued analytic functions on the open unit disc and estimates on such functions and their derivatives are deduced.

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.

Sign in / Sign up

Export Citation Format

Share Document