scholarly journals Certain sufficient conditions for close-to-convexity and starlikeness of multivalent functions

2020 ◽  
Vol 23 (2) ◽  
pp. 201-210
Author(s):  
Mohamed K. Aouf ◽  
Teodor Bulboacă ◽  
Adela O. Mostafa
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Jack’S Lemma ◽  
Jack's Lemma

By using Jack's lemma, we derive simple sufficient conditions for analytic functions to be multivalent close-to-convex and multivalent starlike.

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 A Note on the Class of Functions with Bounded Turning

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Adem Kılıçman
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Analytic Functions ◽  
Geometric Representation ◽  
Jack’S Lemma ◽  
Bounded Turning ◽  
Class Of Functions ◽  
Jack's Lemma

We consider subclasses of functions with bounded turning for normalized analytic functions in the unit disk. The geometric representation is introduced, some subordination relations are suggested, and the upper bound of the pre-Schwarzian norm for these functions is computed. Moreover, by employing Jack's lemma, we obtain a convex class in the class of functions of bounded turning and relations with other classes are posed.

scholarly journals On a local version of Jack’s lemma

2019 ◽  
Vol 27 (2) ◽  
pp. 101-108
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół
Keyword(s):  
Analytic Functions ◽  
Boundary Behavior ◽  
Local Version ◽  
Jack’S Lemma ◽  
Jack's Lemma

AbstractThe purpose of this paper is to provide a result which concerns with the boundary behavior of analytic functions. It may be a local version of the well known Jack’s lemma when we change the function normalization at the origin.

Neighborhoods for certain analytic functions

2016 ◽  
Vol 09 (04) ◽  
pp. 1650083
Author(s):  
Y. Talafha ◽  
B. A. Frasin ◽  
Tariq Al-Hawary ◽  
R. Bani Ata
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Necessary Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Jack’S Lemma ◽  
Sufficient And Necessary Conditions ◽  
Jack's Lemma

In this paper, we introduce the neighborhood [Formula: see text] of analytic functions [Formula: see text] and [Formula: see text] defined in the open unit disc. Furthermore, we derive some sufficient and necessary conditions to be in [Formula: see text]. In addition, we see some applications of Jack’s lemma.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 160
Author(s):  
Likai Liu ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Lemniscate Of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

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