Research Article

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

Volume: 68 Number: 2 August 1, 2019
EN

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

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

References

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Duren P.L., Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983.
  6. 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.
  7. 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.
  8. Lewin M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., Vol.18 (1967), 63--68.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

August 1, 2019

Submission Date

December 30, 2018

Acceptance Date

January 14, 2019

Published in Issue

Year 2019 Volume: 68 Number: 2

APA
Güney, H., Murugusundaramoorthy, G., & Sokol, J. (2019). Certain subclasses of bi-univalent functions related to k-Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1909-1921. https://doi.org/10.31801/cfsuasmas.505287
AMA
1.Güney H, Murugusundaramoorthy G, Sokol J. Certain subclasses of bi-univalent functions related to k-Fibonacci numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1909-1921. doi:10.31801/cfsuasmas.505287
Chicago
Güney, H.özlem, G. Murugusundaramoorthy, and Janusz Sokol. 2019. “Certain Subclasses of Bi-Univalent Functions Related to K-Fibonacci Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2): 1909-21. https://doi.org/10.31801/cfsuasmas.505287.
EndNote
Güney H, Murugusundaramoorthy G, Sokol J (August 1, 2019) Certain subclasses of bi-univalent functions related to k-Fibonacci numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1909–1921.
IEEE
[1]H. Güney, G. Murugusundaramoorthy, and J. Sokol, “Certain subclasses of bi-univalent functions related to k-Fibonacci numbers”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1909–1921, Aug. 2019, doi: 10.31801/cfsuasmas.505287.
ISNAD
Güney, H.özlem - Murugusundaramoorthy, G. - Sokol, Janusz. “Certain Subclasses of Bi-Univalent Functions Related to K-Fibonacci Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 1, 2019): 1909-1921. https://doi.org/10.31801/cfsuasmas.505287.
JAMA
1.Güney H, Murugusundaramoorthy G, Sokol J. Certain subclasses of bi-univalent functions related to k-Fibonacci numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1909–1921.
MLA
Güney, H.özlem, et al. “Certain Subclasses of Bi-Univalent Functions Related to K-Fibonacci Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, Aug. 2019, pp. 1909-21, doi:10.31801/cfsuasmas.505287.
Vancouver
1.H.özlem Güney, G. Murugusundaramoorthy, Janusz Sokol. Certain subclasses of bi-univalent functions related to k-Fibonacci numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019 Aug. 1;68(2):1909-21. doi:10.31801/cfsuasmas.505287

Cited By

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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