Coefficient Estimates of Certain Subclasses of Bi-Bazilevic Functions Associated with Chebyshev Polynomials and Mittag-Leffler Function
Abstract
In this present investigation, the authors introduced certain subclasses of the function class $ T^{\alpha}_{\theta}(\lambda, \beta, t)$ of bi-Bazilevic univalent functions defined in the open unit disk $U$, which are associated with Chebyshev polynomials and Mittag-Leffler function. We establish the Taylor Maclaurin coefficients $\left|a_{2}\right|$, $\left|a_{3}\right|$ and $\left|a_{4}\right|$ for functions in the new subclass introduced and the Fekete-Szego problem is solved.
References
S. Altinkaya and S. Yalcin, Initial coefficient bounds for a general class of biunivalent functions, International Journal of Analysis 20 (2014), Article ID 867871. https://doi.org/10.1155/2014/867871
S. Altinkaya and S. Yalcin, Coefficient bounds for a subclass of bi-univalent functions, TWMS Journal of Pure and Applied Mathematics 6(2) (2015), 180-185.
S. Altinkaya and S. Yalcin, Coefficient estimates for two new subclasses of biunivalent functions with respect to symmetric points, Journal of Function Spaces 2015 (2015), Article ID 145242. https://doi.org/10.1155/2015/145242
S. Altinkaya and S. Yalcin, On the Chebyshev polynomial coefficient problem of some subclasses of bi-univalent functions, Gulf Journal of Mathematics 5 (2017), 34-40.
B. P. Amol and H. N. Uday, Estimate on coefficients of certain subclasses of bi-univalent functions associated with Hohlov operator, Palestine Journal of Mathematics 7(2) (2018), 487-497.
I. T. Awolere and S. Ibrahim-Tiamiyu, New subclasses of bi-univalent pseudo starlike function using Alhindi-Darus generalized hypergeometric function, Journal of the Nigerian Association of Mathematical Physics 40 (2017), 65-72.
D. A. Brannan, J. Clunie and W. E. Kirwan, Coefficient estimates for a class of star-like functions, Canadian Journal of Mathematics 22 (1970), 476-485. https://doi.org/10.4153/CJM-1970-055-8
D. A. Brannan and J. Clunie (Eds.), Aspects of Contemporary Complex Analysis, Proceedings of the NATO Advanced Study Institute (University of Durham, Durham; July, 1979), Academic Press, New York and London, 1980.
P. L. Duren, Univalent functions, Grundlehren der Math. Wiss. 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
M. Fekete and G. Szego, Eine bemerkung uber ungerade schlichte funktionen, J. London Math. Soc. 8 (1933), 85-89. https://doi.org/10.1112/jlms/s1-8.2.85
B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048
M. Lewin, On the coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68. https://doi.org/10.1090/S0002-9939-1967-0206255-1
G. Mittag-Leffler, Sur la nouvelle fonction $E_{alpha}(x)$, C. R. Acad. Sci. Paris 137 (1903), 554-558.
G. Murugusundaramoorthy, Coefficient estimates of bi-Bazileviuc function of complex order based on quasi subordination involving Srivastava-Attiya operator, 2016. arXiv:1601.0229vl [math.cv]
E. Netanyahu, The minimal distance of the image boundary from origin and second coefficient of a univalent function in $left|zright|<1$, Arch. Ration Mech. Anal. 32 (1969), 100-112. https://doi.org/10.1007/BF00247676
F. Yousef, B. A. Frasin and Tariq Al-Hawary, Fekete-Szego inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials, 2018. arXiv:1801.09531 [math.CV]
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