Application of Pascal Distribution Series to Ronning Type Starlike and Convex Functions

Yıl 2020, Cilt: 4 Sayı: 4, 243 - 251, 30.12.2020

Gangadharan Murugusundaramoorthy

https://doi.org/10.31197/atnaa.743436

Cited By: 2

Öz

 In  this  article  we  investigate  the  connections   between  the  Pascal  distribution  series and   the  class  of  analytic  functions  $ f $   normalized  by  $ f ( 0 ) = f ' ( 0 ) - 1 = 0 $  in  the  open  unit  disk  $ \mathbb { U } = \left \{ z \in \mathbb { C } : | z | < 1 \right \} $  and  its  coefficients are probabilities of the Pascal distribution.More precisely ,we determine such connection with parabolic starlike and uniformly convex functions in the open unit disk $\mathbb{U}$ . 

Anahtar Kelimeler

Starlike functions, Convex functions, Uniformly Starlike functions, Uniformly Convex functions, Hadamard product, Pascal distribution series

Destekleyen Kurum

NOT APPLICALE

Kaynakça

• [1] R. M. Ali, K. G. Subramanian, V. Ravichandran, and Om P. Ahuja,Neighborhoods of starlike and convex functions associated with parabola,JIA Volume (2008), Article ID 346279, 9 pages.
• [2] T.Bulboaca and G. Murugusundaramoorthy,Univalent functions with positive coefficients involving Pascal distribution series,Commun. Korean Math. Soc. (accepted for publications-2020 ,https://doi.org/10.4134/CKMS.c190413)
• [3] R.Bharati,R.Parvatham and A.Swaminathan,On subclasses of uniformly convex functions and corresponding class of starlike functions,Tamkang J.Math., 26(1)(1997), 17-32.
• [4] N.E. Cho, S.Y.Woo and S. Owa, Uniform convexity properties for hypergeometric functions, Fract. Cal. Appl. Anal., 5(3) (2002),303-313.
• [5] S. M. El-Deeb,T.Bulboaca and J. Dziok,Pascal Distribution Series Connected with Certain Subclasses of Univalent Functions,Kyungpook Math. J. 59(2019), 301-314
• [6] E. Merkes and B.T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), 885-888.
• [7] 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.
• [8] G.Murugusundaramoorthy, B.A.Frasin and T.Al-Hawary,Uniformly convex spiral functions and uniformly spirallike function associated with Pascal distribution series, arXiv:2001.07517v1,(2020),1-10.
• [9] G. Murugusundaramoorthy , K. Vijaya and K. Uma, Subordination results for a class of analytic functions involving the Hurwitz-Lerch zeta function,Inter. J. of Nonlinear Sci.,Vol.10(2010) no.4,430-437.
• [10] G. Murugusundaramoorthy , K. Vijaya and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series,Hacet.J.Math.Stat. 45 (2016), no.4,1101-1107.
• [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.
• [13] H.Silverman, Univalent functions with negative coefficients, Proc.Amer.Math.Soc.,51 (1975), 109-116.
• [14] K.G.Subramanian, G.Murugusundaramoorthy, P.Balasubrahmanyam and H.Silverman, Subclasses of uniformly convex and uniformly starlike functions., Math.Japonica 42(3), (1995), 517-522.
• [15] T.Rosy, B.A. Stephen, K.G. Subramanian and H.Silverman, Classes of convex functions. Internat. J. Math., Math. Sci. 23(12), (2000), 819–825.
• [16] 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.
• [17] A.Swaminathan, Certain sufficient conditions on Gaussian hypergeometric functions, Journal of Inequalities in Pure and Applied Mathematics., 5(4), Art.83 (2004), 1-10.