An Extension of Jack’s Lemma to Polynomials of Fixed Degree

2007 ◽  
Vol 7 (2) ◽  
pp. 371-378 ◽  
Author(s):  
Richard Fournier ◽  
Marius Serban
Keyword(s):  
Fixed Degree ◽  
Jack’S Lemma ◽  
Jack's Lemma

scholarly journals Applications of the Jack's lemma for the meromorphic functions at the boundary

2019 ◽  
Vol 38 (7) ◽  
pp. 219-226
Author(s):  
Tugba Akyel ◽  
Bulent Nafi Ornek
Keyword(s):  
Boundary Point ◽  
Meromorphic Functions ◽  
Schwarz Lemma ◽  
Jack’S Lemma ◽  
Boundary Version ◽  
Jack's Lemma ◽  
The Schwarz Lemma

In this paper, a boundary version of the Schwarz lemma for the class $\mathcal{% N(\alpha )}$ is investigated. For the function $f(z)=\frac{1}{z}% +a_{0}+a_{1}z+a_{2}z^{2}+...$ defined in the punctured disc $E$ such that $% f(z)\in \mathcal{N(\alpha )}$, we estimate a modulus of the angular derivative of the function $\frac{zf^{\prime }(z)}{f(z)}$ at the boundary point $c$ with $\frac{cf^{\prime }(c)}{f(c)}=\frac{1-2\beta }{\beta }$. Moreover, Schwarz lemma for class $\mathcal{N(\alpha )}$ is given.

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 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.

Applications of the Jack's lemma for the holomorphic functions

2018 ◽  
Vol 48 (2) ◽  
pp. 125-139
Author(s):  
Bülent Nafi Örnek ◽  
Selin Aydınoğlu
Keyword(s):  
Holomorphic Functions ◽  
Jack’S Lemma ◽  
Jack's Lemma

On Jack's lemma

2019 ◽  
Vol 49 (6) ◽  
pp. 1869-1875
Author(s):  
Richard Fournier
Keyword(s):  
Jack’S Lemma ◽  
Jack's Lemma

On a new proof and an extension of Jack’s lemma

2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Richard Fournier
Keyword(s):  
Jack’S Lemma ◽  
Jack's Lemma

AbstractWe give a new proof and discuss an extension of Jack’s lemma for polynomials.

scholarly journals Jack’s lemma for certain subclasses of analytic functions defined by a new fractional linear operator

2017 ◽  
Author(s):  
Zainab E. Abdulnaby ◽  
Rabha W. Ibrahim ◽  
Adem Kılıçman
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Jack’S Lemma ◽  
Jack's Lemma

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.

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