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A Class of Complex-valued Harmonic Functions Defined by Dziok-Srivastava Operator

CJM Vol. 1 No. 2 (December 2009) [1], pp. 31 – 42.

Author(s): 
R. Chandrashekar [2]
G. Murugusundaramoorthy [3]
S.K. Lee [4]
K.G. Subramanian [5]

Abstract: 

The Dziok-Srivastava [6] operator introduced in the study of analytic functions and associated with generalized hypergeometric functions has been extended to harmonic mappings [2, 12]. Using this operator we introduce a subclass of the class $\mathcal{H}$ of complex-valued harmonic univalent functions $f = h +\bar{g}$ where $h$ is the analytic part and $g$ is the co-analytic part of $f$ in $|z| < 1$. Coefficient bounds, extreme points, inclusion results and closure under an integral operator for this class are obtained.

Keywords: 
Harmonic functions [6]
Hypergeometric functions [7]
Dziok-Srivastava operator [8]
extreme points [9]
integral operator [10]

2000 Mathematics Subject Classification: 
30C45 [11]
30C50 [12]

Full Paper (PDF): 
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PDF icon 03-2-CJM2009-022-GP.pdf [13]256.96 KB

Source URL: http://math.sc.chula.ac.th/cjm/content/class-complex-valued-harmonic-functions-defined-dziok-srivastava-operator

Links
[1] http://www.math.sc.chula.ac.th/cjm/vol1no2
[2] http://math.sc.chula.ac.th/cjm/tags/r-chandrashekar
[3] http://math.sc.chula.ac.th/cjm/tags/g-murugusundaramoorthy
[4] http://math.sc.chula.ac.th/cjm/tags/sk-lee
[5] http://math.sc.chula.ac.th/cjm/tags/kg-subramanian
[6] http://math.sc.chula.ac.th/cjm/tags/harmonic-functions
[7] http://math.sc.chula.ac.th/cjm/tags/hypergeometric-functions
[8] http://math.sc.chula.ac.th/cjm/tags/dziok-srivastava-operator
[9] http://math.sc.chula.ac.th/cjm/tags/extreme-points
[10] http://math.sc.chula.ac.th/cjm/tags/integral-operator
[11] http://math.sc.chula.ac.th/cjm/tags/30c45
[12] http://math.sc.chula.ac.th/cjm/tags/30c50
[13] https://d2ijd3g5wqapxj.cloudfront.net/cjm/sites/www.math.sc.chula.ac.th.cjm/files/03-2-CJM2009-022-GP.pdf