Bulletin of the Belgian Mathematical Society - Simon Stevin

Convolution of Harmonic Mappings On The Exterior Unit Disk and the Generalized Hypergeometric Functions

Rosihan M. Ali, B. Adolf Stephen, K. G. Subramanian, and S. K. Lee

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Abstract

A new class is introduced consisting of harmonic univalent functions on the exterior unit disk defined by convolution. This class generates several known and new subclasses of harmonic univalent functions as special cases. A necessary and sufficient convolution condition is obtained for functions to belong to the class. A corresponding general class of harmonic functions with negative coefficients is also introduced, and coefficient condition that is both necessary and sufficient is obtained for the class. Extreme points are also determined. As applications, starlikeness conditions of the Liu-Srivastava linear operator involving the generalized hypergeometric functions are discussed.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 2 (2011), 239-251.

Dates
First available in Project Euclid: 7 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1307452074

Digital Object Identifier
doi:10.36045/bbms/1307452074

Mathematical Reviews number (MathSciNet)
MR2847760

Zentralblatt MATH identifier
1218.30015

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C55: General theory of univalent and multivalent functions 58E20: Harmonic maps [See also 53C43], etc.

Keywords
Harmonic functions convolution harmonic starlike and convex functions negative coefficients Liu-Srivastava operator generalized hypergeometric functions

Citation

Ali, Rosihan M.; Stephen, B. Adolf; Subramanian, K. G.; Lee, S. K. Convolution of Harmonic Mappings On The Exterior Unit Disk and the Generalized Hypergeometric Functions. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 2, 239--251. doi:10.36045/bbms/1307452074. https://projecteuclid.org/euclid.bbms/1307452074


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