The distortion theorem for holomorphic convex and starlike mappings

1998 ◽  
pp. 137-169
Author(s):  
Sheng Gong
Keyword(s):  
Distortion Theorem ◽  
Starlike Mappings

scholarly journals Some properties of univalent log-harmonic mappings

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5275-5288 ◽  
Author(s):  
Zhihong Liu ◽  
Saminathan Ponnusamy
Keyword(s):  
Representation Theorem ◽  
Distortion Theorem ◽  
Harmonic Mappings ◽  
Schwarzian Derivatives ◽  
Starlike Mappings ◽  
Harmonic Starlike ◽  
Coefficients Estimate

We determine the representation theorem, distortion theorem, coefficients estimate and Bohr?s radius for log-harmonic starlike mappings of order ?, which are generalization of some earlier results. In addition, the inner mapping radius of log-harmonic mappings is also established by constructing a family of 1-slit log-harmonic mappings. Finally, we introduce pre-Schwarzian, Schwarzian derivatives and Bloch?s norm for non-vanishing log-harmonic mappings, several properties related to these are also obtained.

scholarly journals A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Convolution Operator ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Open Unit Disc ◽  
Coefficient Inequalities ◽  
Uniformly Starlike Functions ◽  
Convex And Starlike Functions ◽  
Uniformly Starlike

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.

Parabolic starlike mappings in several complex variables

2007 ◽  
Vol 123 (3) ◽  
pp. 301-324 ◽  
Author(s):  
Hidetaka Hamada ◽  
Tatsuhiro Honda ◽  
Gabriela Kohr
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Starlike Mappings

On Logarithmic Derivatives of Functions in a Class of Starlike Mappings

1993 ◽  
Vol 36 (1) ◽  
pp. 38-44
Author(s):  
Alan D. Gluchoff
Keyword(s):  
Integral Means ◽  
Koebe Function ◽  
Starlike Mappings ◽  
Derivatives Of ◽  
Logarithmic Derivatives

AbstractThe purpose of this paper is to prove some facts about integral means of (d2/dz2)(log[f(z)/z])—or equivalently f″/f, for f in a class of starlike mappings of a "singular" nature. In particular it is noted that the Koebe function is not extremal for the Hardy means Mp(r,f″/f) for functions in this class.

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