Coefficient estimates for a class of meromorphic bi-univalent functions

Subject Areas : Statistics

Safa  Salehian ¹ (Department of Mathematics. Gorgan Branch. Islamic Azad University, Gorgan, Iran)
Ahmad  Motamednezhad ² (Faculty of Mathematical Sciences, Shahrood University of Technology, P.O.Box 316-36155, Shahrood, Iran)

Received: 2018-10-13 Accepted : 2020-04-19 Published : 2020-07-01

Keywords: توابع دو- تک ارز مرومورفیک, چند جمله ای فابر, تقریب ضرایب, توابع مرومورفیک, مشتق q-ام,

Abstract :

Let 𝝨 be the class of meromorphic bi-univalent functions f of the formf(z)=z+b_0+∑_(n=1)^∞▒b_n/z^n ,which are univalent (analytic and one to one) on the domain Δ={z∈C∶1

References:

[1] H‎. ‎Airault, A‎. ‎Bouali.  ‎Differential Calculus on the faber polynomials. Bull. Sci. Math. 130 (3): 179-222 (2006).‎

 

[2] H‎. ‎Airault‎, ‎J‎. ‎Ren. ‎An algebra of differential operators and generating functions on the set of univalent functions. Bull. Sci. Math. ‎126(5): 343-367(2002).‎

 

[3] ‎S. ‎Bulut‎, ‎N‎. ‎Magesh, V‎. ‎K‎. ‎Balaji‎. Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions‎. Comptes Rendus Mathematique.‎ ‎353(2): 113-116(2015).‎

 

[4] P‎. ‎L‎. ‎Duren. Univalent functions‎, ‎Grundlehren der Mathematischen‎, ‎Band 259‎, ‎Springer‎, ‎Tokyo‎, ‎1983.‎

 

[5] S. ‎G‎. ‎Hamidi‎, ‎S‎. ‎A‎. ‎Halim, J‎. ‎M‎. ‎Jahangiri.  ‎Coefficient estimates for a class of meromorphic bi-univalent ‎‎functions‎. Comptes Rendus Mathematique 351: 349-352 (2013).‎

 

[6] T‎. ‎Janani, G‎. ‎MurugusundaraMoor-thy‎. ‎Coefficient estimates of meromorphic bi-starlike functions of‎‎ complex order. Internat. J. Anal. Appl. 4 (1): 68-77‎(2014).

 

[7] G‎. ‎P‎. ‎Kapoor,  A‎. ‎K‎. ‎Mishr. Coefficient estimates for inverses of starlike functions of positive ‎‎order. ‎‎J‎. ‎Math‎.  nal. ‎Appl., ‎329(2): 922-934 (2007).‎

 

[8] J. ‎G‎. ‎Krzyz‎, ‎R‎. ‎J‎. ‎Libera, E‎. ‎J‎. ‎Zlotkiewicz. ‎Coefficients of inverse of regular starlike functions‎. ‎Ann.‎‎ Univ‎. ‎Mariae Curie-Skodowska Sect‎. ‎A‎ ‎33: 103-109(1979).

 

[9] Y. ‎Kubota‎. ‎Coefficients of meromorphic univalent functions‎. ‎Kōdai Math‎. ‎Sem‎.Rep. ‎28: 253-261‎ (1976).

 

[10] G‎. ‎Schober‎. ‎Coefficients of inverses of meromorphic univalent functions‎.‎ Proc‎. ‎Amer‎. Math‎. Soc.‎ ‎67(1): 111-116 (1977)‎‎.

 

[11] M. Schiffer, Sur Un problème d’xtrémum de la representation conforme. Bull. Soc. Math. France., 66: 48-55 (1938).

 

[12] H. M. Srivastava, Ş. ‎Altınkaya, S. ‎Yalçın.  ‎Hankel ‎d‎eterminant for a s‎ubclass of b‎i-‎‎nivalent ‎f‎unctions ‎d‎efined by ‎u‎sing  a ‎s‎ymmetric q-‎d‎erivative ‎operator,‎ Filomat, ‎32(2): 503–51‎6‎.‎ (2018).

‎

[13] Q.-H‎.‎ Xu, H‎. ‎M‎. Srivastava. Coefficient estimates for the inverses of a certain general class‎‎ of spirallike functions, ‎Appl‎. ‎Math‎. ‎Comput.‎, 219: 7000-7011(2013).‎

 

[14] H.-G‎. ‎Xiao, Q.-‎. ‎Xu‎, ‎Coefficient estimates for three generalized classes of meromorphic and bi-univalent functions‎, ‎Filomat‎, ‎29 (7): 1601-1612 (2015) .