scholarly journals On coefficients of some p-valent starlike functions

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2277-2284
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół ◽  
Nikola Tuneski
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Unit Disc ◽  
Satisfying Condition ◽  
Starlike Functions

We consider the class Ap of functions f analytic in the unit disk |z| < 1 in the complex plane, of the form f(z) = zp + ... such that Rezf(p)(z)/f (p-1)(z) > 0 in the unit disc. The object of the present paper is to derive some bounds for coefficients in this class and relation with the functions satisfying condition Ref(k)(z)/f(p-k)(z) > 0 in the unit disc.

scholarly journals Growth Theorems for a Subclass of Strongly Spirallike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yan-Yan Cui ◽  
Chao-Jun Wang ◽  
Si-Feng Zhu
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Starlike Functions ◽  
Geometric Properties ◽  
Strongly Starlike Functions ◽  
Strongly Starlike ◽  
Spirallike Functions ◽  
Analytic Mappings

In this paper we consider a subclass of strongly spirallike functions on the unit diskDin the complex planeC, namely, strongly almost spirallike functions of typeβand orderα. We obtain the growth results for strongly almost spirallike functions of typeβand orderαon the unit diskDinCby using subordination principles and the geometric properties of analytic mappings. Furthermore we get the growth theorems for strongly almost starlike functions of orderαand strongly starlike functions on the unit diskDofC. These growth results follow the deviation results of these functions.

A Class of Analytic Starlike Functions Associated with Petal Like Region on the Positive Half of Complex Plane

2020 ◽  
Vol 87 (3-4) ◽  
pp. 165
Author(s):  
Rajesh Kumar Maurya ◽  
Poonam Sharma
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Algebraic Structure ◽  
Starlike Functions ◽  
Open Mapping ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Open Mapping Theorem ◽  
Positive Half

In the light of Riemann open mapping theorem, if we map open unit disk U conformally onto a region then depending on the geometry of boundary of we can always extract a subclass of H[a, n] by subordinating various functionals of the function f ∈ H[a, n]. Depending upon the geometry of the range set attempts have been made to find some algebraic structure in such classes, for that Hankel determinant of coefficients of functions pertaining to these classes have been studied, bounds of various coefficients have been determined and also based on the subordination principle we have determined radius |z| &lt; r ;z ∈ U for which f belongs to such a class. In this paper our focus would be on n−PS<sup>*</sup> defined as n − PS<sup>*</sup> = {f ∈ A : Re {zf<sup>'</sup>(z)/f(z)} &gt; 0,|(zf<sup>'</sup>(z)/f(z))<sup>n</sup> - 1|&lt;1}.

Starlike functions associated with a lune

2017 ◽  
Vol 10 (04) ◽  
pp. 1750064 ◽  
Author(s):  
Shweta Gandhi ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Half Plane ◽  
Complex Plane ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Lemniscate Of Bernoulli ◽  
The Right

Several subclasses of starlike functions are associated with regions in the right half plane of the complex plane, like half-plane, disks, sectors, parabolas and lemniscate of Bernoulli. For a normalized analytic function [Formula: see text] defined on the open unit disk [Formula: see text] belonging to certain well-known classes of functions associated with the above regions, we investigate the radius [Formula: see text] such that, for the function [Formula: see text], [Formula: see text] lies in the lune defined by [Formula: see text] for all [Formula: see text].

scholarly journals Strongly Starlike Functions and Related Classes

2021 ◽  
Vol 52 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokol
Keyword(s):  
Complex Plane ◽  
Unit Disc ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Nice Property ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

We consider  univalent functions, analytic in the unit disc $ |z|<1$in the complex plane ${\mathbb{C}}$ which map $ |z|<1$ onto a domainwith some nice property. The purpose of this paper is to find somenew conditions for strong starlikeness and some related results.

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.

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 A note on n-harmonic majorants

1986 ◽  
Vol 34 (3) ◽  
pp. 461-472
Author(s):  
Hong Oh Kim ◽  
Chang Ock Lee
Keyword(s):  
Harmonic Function ◽  
Complex Plane ◽  
Unit Disc ◽  
Dirichlet Integral ◽  
Harmonic Majorant ◽  
Harmonic Majorants

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.

scholarly journals A note on a space Hp, a of holomorphic functions

1987 ◽  
Vol 35 (3) ◽  
pp. 471-479
Author(s):  
H. O. Kim ◽  
S. M. Kim ◽  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Complex Plane ◽  
Unit Disc ◽  
Weak Type ◽  
Holomorphic Functions ◽  
Embedding Theorem ◽  
Type Operator ◽  
Taylor Coefficients ◽  
Bounded Holomorphic

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

scholarly journals On the Fekete-Szegö problem

2000 ◽  
Vol 24 (9) ◽  
pp. 577-581 ◽  
Author(s):  
B. A. Frasin ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

On BMOA for Riemann Surfaces

1981 ◽  
Vol 33 (5) ◽  
pp. 1255-1260 ◽  
Author(s):  
Thomas A. Metzger
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Hardy Class ◽  
Image Position

Let Δ denote the unit disk in the complex plane C. The space BMO has been extensively studied by many authors (see [3] for a good exposition of this topic). Recently, the subspace BMOA (Δ) has become a topic of interest. An analytic function f, in the Hardy class H2(A), belongs to BMOA (Δ) if(1)whereIt is known (see [3, p. 96]) that (1) is equivalent to(2)

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