scholarly journals Majorization Results for Certain Subfamilies of Analytic Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Muhammad Arif ◽  
Miraj Ul-Haq ◽  
Omar Barukab ◽  
Sher Afzal Khan ◽  
Saleem Abullah
Keyword(s):  
Holomorphic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Open Unit Disc

Let h 1 z and h 2 z be two nonvanishing holomorphic functions in the open unit disc with h 1 0 = h 2 0 = 1 . For some holomorphic function q z , we consider the class consisting of normalized holomorphic functions f whose ratios f z / z q z and q z are subordinate to h 1 z and h 2 z , respectively. The majorization results are obtained for this class when h 1 z is chosen either h 1 z = cos z or h 1 z = 1 + sin z or h 1 z = 1 + z and h 2 z = 1 + sin z .

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.

scholarly journals Subordination and superordination results of p-valent analytic functions involving a linear operator

2017 ◽  
Vol 35 (2) ◽  
pp. 223 ◽  
Author(s):  
Tamer M. Seoudy
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of a linear operator. Some of our results improve and generalize previously known results.

Majorization-Subordination Theorems for Locally Univalent Functions, II

1973 ◽  
Vol 25 (2) ◽  
pp. 420-425 ◽  
Author(s):  
Douglas Michael Campbell
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Family ◽  
Linear Invariant ◽  
Linear Invariant Family

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]

scholarly journals Convolution Properties for Certain Classes of Analytic Functions Defined byq-Derivative Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Convolution Properties

We investigate convolution properties and coefficients estimates for two classes of analytic functions involving theq-derivative operator defined in the open unit disc. Some of our results improve previously known results.

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 Best Dominants and Subordinants for Certain Sandwich-Type Theorems

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 62
Author(s):  
Adriana Cătaş ◽  
Emilia Borşa ◽  
Loredana Iambor
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Symmetric Domain ◽  
Open Unit ◽  
Open Unit Disc ◽  
Sandwich Type

In this paper, we aim to present a survey on subordination and superordination theorems related to the class of analytic functions defined in a symmetric domain, which is the open unit disc. The results were deduced by making use of a new differential operator. We present two properties of this operator from which we constructed the final results. Moreover, based on the obtained outcomes, we give two sandwich-type theorems. Some interesting further consequences are also taken into consideration.

scholarly journals Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 105
Author(s):  
Abdel Moneim Y. Lashin ◽  
Badriah Maeed Algethami ◽  
Abeer O. Badghaish
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Inclusion Properties ◽  
Convolution Properties

In this paper, the Jackson q-derivative is used to investigate two classes of analytic functions in the open unit disc. The coefficient conditions and inclusion properties of the functions in these classes are established by convolution methods.

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.

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