COEFFICIENT BOUNDS USING FABER POLYNOMIAL FOR A NEW SUBCLASS OF MEROMORPHIC BI-UNIVALENT FUNCTIONS
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A recently introduced subclass of meromorphic bi-univalent functions class $\Sigma'$ is considered for the study and coefficient estimates $|b_0|, |b_1|$ and $|b_2|$ are determined in the present investigation. Further, the coefficient estimate $|b_n|$ is obtained for functions in the new subclass $\Sigma'$ using Faber polynomials. Various remarks of the results are also specified in generalized form.
Abstract
A recently introduced subclass of meromorphic bi-univalent functions class $\Sigma'$ is considered for the study and coefficient estimates $|b_0|, |b_1|$ and $|b_2|$ are determined in the present investigation. Further, the coefficient estimate $|b_n|$ is obtained for functions in the new subclass $\Sigma'$ using Faber polynomials. Various remarks of the results are also specified in generalized form.
참고문헌 (19)
- H. Airault, "Differential calculus on the Faber polynomials", Bull. Sci. Math, 130(3), pp.179~222 (2006)[DOI]
- H. Airault, "An algebra of differential operators and generating functions on the set of univalent functions", Bull. Sci. Math, 126(5), pp.343~367 (2002)[DOI]
- A. Bouali, "Faber polynomials, Cayley-Hamilton equation and Newton symmetric functions", Bull. Sci. Math, 130(1), pp.49~70 (2006)[DOI]
- E. Deniz, "Certain subclasses of bi-univalent functions satisfying subordinate conditions", J. Class. Anal, 2(1), pp.49~60 (2013)[DOI]
- P. L. Duren, "Coefficients of meromorphic schlicht functions", Proc. Amer. Math. Soc, 28, pp.169~172 (1971)[DOI]
- G. Faber, "¨ Uber polynomische Entwickelungen", Math. Ann, 57, pp.389~408 (1903)
- S. G. Hamidi, "Faber polynomial coefficient estimates for meromorphic bi-starlike functions", Int. J. Math. Math. Sci, pp.4~ (2013)[DOI]
- S. G. Hamidi, "Coefficent estimates for bi-univalent strongly starlike and Bazilevic functions", Int. J. Math. Math. Res, 5(1), pp.87~96 (2013)
- S. G. Hamidi, "Coefficient estimates for certain classes of meromorphic bi-univalent functions", C. R. Math. Acad. Sci. Paris, 352(4), pp.277~282 (2014)[DOI]
- T. Janani, "New subclass of pseudo-type meromorphic bi-univalent functions of complex order", Novi Sad J. Math, 48(1), pp.93~102 (2018)[DOI]
- T. Janani, "Advances in Algebra and Analysis, Trends in Mathematics, Volume I", pp.151~159 (2018)
- G. P. Kapoor, "Coefficient estimates for inverses of starlike functions of positive order", J. Math. Anal. Appl, 329(2), pp.922~934 (2007)[DOI]
- Y. Kubota, "Coefficients of meromorphic univalent functions", Kodai Math. Sem. Rep, 28(2-3), pp.253~261 (1976)
- Mathematische Lehrb¨ucher, Band XXV, "Studia Mathematica", pp.1975, C. Pommerenke
- M. Schiffer, "Sur un probl`eme d’extr´emum de la repr´esentation conforme", Bull. Soc. Math. France, 66, pp.48~55 (1938)
- G. Schober, "Coefficients of inverses of meromorphic univalent functions", Proc. Amer. Math. Soc, 67(1), pp.111~116 (1977)[DOI]
- G. Springer, "The coefficient problem for schlicht mappings of the exterior of the unit circle", Trans. Amer. Math. Soc, 70, pp.421~450 (1951)[DOI]
- H. M. Srivastava, "Coefficient estimates for the inverses of starlike functions represented by symmetric gap series", PanAmer. Math. J, 21(4), pp.105~123 (2011)
- P. G. Todorov, "On the Faber polynomials of the univalent functions of class Σ", J. Math. Anal. Appl, 162(1), pp.268~276 (1991)[DOI]