scholarly journals Generalizedk-Uniformly Close-to-Convex Functions Associated with Conic Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Problems ◽  
Multiplier Transformation ◽  
Inclusion Results

We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible.

scholarly journals Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Subordination Result ◽  
Jack’S Lemma ◽  
Jack's Lemma

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

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 Functions starlike with respect to other points

1991 ◽  
Vol 14 (3) ◽  
pp. 451-456 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Real ◽  
Symmetric Points ◽  
Class Of Functions

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. Forp≤β<1, letSS*(β)be the class of normalised analytic functionsfdefined in the open unit discDsuch thatRezf′(z)/(f(z)−f(−z))>β, for somez ϵ D. In this paper, we introduce 2 other similar classesSC*(β),SSC*(β)as well as give sharp results for the real part of some function forf ϵ SS*(β),SC*(β)andSSC*(β)The behaviour of certain integral operators are also considered.

scholarly journals Some classes of p-valent analytic functions associated with hypergeometric functions

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1031-1038 ◽  
Author(s):  
Khalida Noor ◽  
Nasir Khan
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class A ◽  
Radius Problem ◽  
Inclusion Results

We define a linear operator on the class A(p) of p-valent analytic functions in the open unit disc involving Gauss hypergeometric functions and introduce certain new subclasses of A(p) using this operator. Some inclusion results, a radius problem and several other interesting properties of these classes are studied.

A generalized class of α-convex functions with respect to n-symmetric points

2021 ◽  
pp. 2250099
Author(s):  
A. Y. Lashin ◽  
F. Z. El-Emam
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Symmetric Points

In this paper, we investigate certain subclass of analytic functions on the open unit disc. This class generalizes the well-known class of [Formula: see text]-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

scholarly journals A note on Bazilevič functions

1991 ◽  
Vol 14 (4) ◽  
pp. 821-823 ◽  
Author(s):  
S. A. Halim ◽  
D. K. Thomas
Keyword(s):  
Lower Bound ◽  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Iterated Integral ◽  
Bazilevic Functions ◽  
Sharp Lower Bound

Forα>0, letB1(α)be the class of normalized analytic functions defined in the open unit discDsatisfyingRe(f(z)/z)α−1f′(z)>0forz∈D. The sharp lower bound forRe(f(z)/z)αis obtained and the result is generalized to some iterated integral operators.

scholarly journals A certain class of q-close-to-convex functions of order α

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2295-2305
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Bieberbach Conjecture ◽  
Gaussian Hypergeometric Function ◽  
Geometric Properties

For every 0 < q < 1 and 0 ? ? < 1, we introduce a class of analytic functions f on the open unit disc D with the standard normalization f(0)= 0 = f'(0)-1 and satisfying |1/1-?(z(Dqf)(z)/h(z)-?)- 1/1-q,(z?D), where h?S*q. This class is denoted by Kq(?), so called the class of q-close-to-convex-functions of order ?. In this paper, we study some geometric properties of this class. In addition, we consider the famous Bieberbach conjecture problem on coefficients for the class Kq(?). We also find some sufficient conditions for the function to be in Kq(?) for some particular choices of the functions h. Finally, we provide some applications on q-analogue of Gaussian hypergeometric function.

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).

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 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.

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