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http://dx.doi.org/10.5831/HMJ.2018.40.3.529

UNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING POISSON DISTRIBUTION SERIES  

Murugusundaramoorthy, Gangadharan (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology)
Publication Information
Honam Mathematical Journal / v.40, no.3, 2018 , pp. 529-538 More about this Journal
Abstract
The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise,we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk.
Keywords
univalent; starlike functions; convex functions; Hadamard product; Poisson distribution;
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1 T. R. Caplinger and W. M. Causey,A class of univalent functions, Proc. Amer. Math. Soc. 39 (1973), 357-361.   DOI
2 N. E. Cho, S. Y. Woo and S. Owa,Uniform convexity properties for hypergeometric functions, Fract. Cal. Appl. Anal., 5(3) (2002), 303-313.
3 L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152.   DOI
4 K. K.Dixit and V.Chandra,On subclass of univalent functions with positive coefficients, Aligarh Bull. Math., 27(2) 2008, 87-93.
5 K. K. Dixit and S. K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math. 26(9)(1995), 889-896.
6 K. K.Dixit and A. L. Pathak, A new class of analytic functions with positive coefficients, Indian J. Pure Appl. Math., 34 (2) (2003),209-218.
7 E. Merkes and B. T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), 885-888.   DOI
8 A. O. Mostafa,A study on starlike and convex properties for hypergeometric functions, J. Inequal. Pure Appl. Math., 10(3) (2009), Art., 87, 1-16.
9 G. Murugusundaramoorthy , K. Vijaya and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacettepe J. Math. Stat. 45(4), 2016, 1101-1107.
10 K. S. Padmanabhan, On a certain class of functions whose derivatives have a positive real part in the unit disc, Ann. Polon. Math. 23 (1970), 73-81.   DOI
11 S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal., Vol.(2014), Art. ID 984135, 1-3.
12 H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl., 172 (1993), 574-581.   DOI
13 H. M. Srivastava, G. Murugusundaramoorthy and S. Sivasubramanian, Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integral Transform Spec. Funct. 18(2007), 511-520.   DOI
14 B. A.Uralegaddi, M. D Ganigi and S. M.Sarangi, Univalent functions with positive coefficients, Tamkang J. Math., 25 (1994), 225-230.