Certain subclasses of bi-univalent functions related to k-Fibonacci numbers

Year 2019, Volume: 68 Issue: 2, 1909 - 1921, 01.08.2019

H.özlem Güney G. Murugusundaramoorthy Janusz Sokol

https://doi.org/10.31801/cfsuasmas.505287

Cited By: 8

Abstract

In this paper, we introduce and investigate new subclasses of bi-univalent

functions related to k-Fibonacci numbers. Furthermore, we nd estimates of first two

coecients of functions in these classes. Also, we obtain the Fekete-Szego inequalities

for these function classes.

Keywords

Analytic functions, bi-univalent, k-fibonacci numbers, starlike function, convex function

References

• Brannan D.A., Clunie J. and Kirwan W.E., Coefficient estimates for a class of star-like functions, Canad. J. Math., Vol.22 (1970), 476--485.
• Brannan D.A. and Taha T.S., On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math., Vol. 31, No.2 (1986), 70--77.
• Bulut S., Certain subclasses of analytic and bi-univalent functions involving the q-derivative operator, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., Vol.66 (2017), 108--114.
• Çaglar M. and Deniz E., Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., Vol.66 (2017), 85--91.
• Duren P.L., Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983.
• Güney H.Ö., Murugusundaramoorthy G. and Sokół J., Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers, Acta Univers. Sapientiae, Mathematica, Vol.10, No.1 (2018), 70--84.
• Güney H.Ö., Sokół J. and İlhan S., Second Hankel determinant problem for some analytic function classes connected with k-Fibonacci numbers, Acta Univers. Apulensis, Vol.54 (2018), 161--174.
• Lewin M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., Vol.18 (1967), 63--68.
• Li X-F. and Wang A-P., Two new subclasses of bi-univalent functions, Inter. Math. Forum, Vol.7, No.30 (2012), 1495--1504.
• Özgür N.Y. and Sokół J., On starlike functions connected with k-Fibonacci numbers, Bull. Malaysian Math. Sci. Soc., Vol.38, No.1 (2015), 249--258.
• Pommerenke, Ch., Univalent Functions, in: Studia Mathematica Mathematische Lehrbucher, Vanderhoeck and Ruprecht, Göttingen, 1975.
• Sokół J., On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis, Vol.175, No.23 (1999), 111--116.
• Sokół J., Remarks on shell-like functions, Folia Scient. Univ. Tech. Resoviensis, Vol.181, No.24 (2000), 111-115.
• Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., Vol.23, No.10 (2010), 1188--1192.
• Xu Q.-H., Gui Y.-C. and Srivastava H.M., Coefficinet estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., Vol.25 (2012), 990--994.
• Zaprawa P., On the Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, Vol.21, No.1 (2014), 169--178.