Integral means and coefficient estimates on planar harmonic mappings

2012 ◽  
Vol 37 ◽  
pp. 69-79 ◽  
Author(s):  
Shaolin Chen ◽  
Saminathan Ponnusamy ◽  
Xiantao Wang
Keyword(s):  
Harmonic Mappings ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Planar Harmonic Mappings

scholarly journals LANDAU’S THEOREM AND MARDEN CONSTANT FOR HARMONIC ν-BLOCH MAPPINGS

2011 ◽  
Vol 84 (1) ◽  
pp. 19-32 ◽  
Author(s):  
SH. CHEN ◽  
S. PONNUSAMY ◽  
X. WANG
Keyword(s):  
Harmonic Mappings ◽  
Coefficient Estimates ◽  
Bloch Functions ◽  
Landau Theorem ◽  
Distortion Theorems ◽  
Planar Harmonic Mappings

AbstractOur main aim is to investigate the properties of harmonic ν-Bloch mappings. Firstly, we establish coefficient estimates and a Landau theorem for harmonic ν-Bloch mappings, which are generalizations of the corresponding results in Bonk et al. [‘Distortion theorems for Bloch functions’, Pacific. J. Math.179 (1997), 241–262] and Chen et al. [‘Bloch constants for planar harmonic mappings’, Proc. Amer. Math. Soc.128 (2000), 3231–3240]. Secondly, we obtain an improved Landau theorem for bounded harmonic mappings. Finally, we obtain a Marden constant for harmonic mappings.

scholarly journals COEFFICIENT ESTIMATES, LANDAU’S THEOREM AND LIPSCHITZ-TYPE SPACES ON PLANAR HARMONIC MAPPINGS

2013 ◽  
Vol 96 (2) ◽  
pp. 198-215 ◽  
Author(s):  
SHAOLIN CHEN ◽  
SAMINATHAN PONNUSAMY ◽  
ANTTI RASILA
Keyword(s):  
Harmonic Mappings ◽  
Coefficient Estimates ◽  
Type Spaces ◽  
Univalent Harmonic Mappings ◽  
Planar Harmonic Mappings

AbstractIn this paper, we investigate the properties of locally univalent and multivalent planar harmonic mappings. First, we discuss coefficient estimates and Landau’s theorem for some classes of locally univalent harmonic mappings, and then we study some Lipschitz-type spaces for locally univalent and multivalent harmonic mappings.

scholarly journals Integral Means and Arc length of Starlike Log-harmonic Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Z. Abdulhadi ◽  
Y. Abu Muhanna
Keyword(s):  
Upper Bound ◽  
Harmonic Mappings ◽  
Arc Length ◽  
Integral Means

We use star functions to determine the integral means for starlike log-harmonic mappings. Moreover, we include the upper bound for the arc length of starlike log-harmonic mappings.

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals Distortion and covering theorems of pluriharmonic mappings

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2749-2762
Author(s):  
Shaolin Chen ◽  
Saminathan Ponnusamy
Keyword(s):  
Analytic Functions ◽  
Harmonic Mappings ◽  
Classical Approach ◽  
Covering Theorems ◽  
Linear Invariant ◽  
Planar Harmonic Mappings

The linear-invariant families of analytic functions make it possible to obtain well-known results to broader classes of functions, and are often helpful in obtaining simpler proofs along with new results. Based on this classical approach due to Pommerenke, properties (such as bounds for the derivative, covering and distortion) of a corresponding class of locally quasiconformal and planar harmonic mappings are established by Starkov. Motivated by these works, in this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

scholarly journals Bloch constants for planar harmonic mappings

2000 ◽  
Vol 128 (11) ◽  
pp. 3231-3240 ◽  
Author(s):  
Huaihui Chen ◽  
P. M. Gauthier ◽  
W. Hengartner
Keyword(s):  
Harmonic Mappings ◽  
Planar Harmonic Mappings
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