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On a new subclass of bi-univalent functions satisfying subordinate conditions

Year 2019, Volume: 68 Issue: 1, 724 - 733, 01.02.2019

Emeka Mazı Sahsene Altınkaya

https://doi.org/10.31801/cfsuasmas.464191
Cited By: 1

Abstract

The purpose of our present paper is to introduce a new subclass of bi-univalent functions associated with pseudo-starlike function with Sakaguchi type functions and to determine the coefficient estimates |a₂| and |a₃| for functions in each of this newly-defined class. We also highlight some known consequences of our main results.

Keywords

Bi-univalent function coefficient bounds pseudo-starlike function. Sakaguchi type function Taylor- Maclaurin coefficients subordination

References

  • Altınkaya, Ş. and Yalçın, S., On a new sublass of bi-univalent functions of Sakaguchi type satisfying subordinate condition, Malaya J. Mat. 5(2), 2017, 305-309.
  • Altınkaya, Ş. and Yalçın, S., Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 6 (2015), 180--185.
  • Altınkaya, Ş. and Yalçın, S., Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015 (2015), Article ID 145242, 1--5.
  • Altınkaya, Ş. and Yalçın, S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris Sér. I 353 (2015), 1075--1080.
  • Ali, R.M., Lee, S.K., Ravichandran, V. and Supramaniam, S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions. Appl. Math. Lett. 25, (2012) 344-351.
  • Babalola, K.O., On λ-pseudo-starlike functions, J. Class. Anal. 3(2), (2013) 137-147.
  • Brannan, D.A. and Clunie, J.G.(Eds.), Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979), Academic Press, New York and London, 1980.
  • Brannan D.A. and Taha, T.S., On some classes of bi-univalent functions Studia Univ. Babe¸s-Bolyai Math, 31(2), (1986).70-77.
  • Duren, P.L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York Berlin Heidelberg and Tokyo, 1983.
  • Frasin, B.A., Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci., 10(2) (2010), 206-211.
  • Goyal, S.P. and Goswami, P., Certain coefficient inequalities for Sakaguchi type functions and applications to fractional derivative operator, Acta Unisarsities Apulensis (No. 1912009)
  • Joshi, S. and Pawar, H., On some subclasses of bi-univalent functions associated with pseudo-starlike functions, Journal of the Egyptian Mathematical Society, 24, (2016), 522-525.
  • Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris Sér. I 354 (2016), 365--370.
  • Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc,18, (1967), 63-68.
  • Murugusundaramoorthy, G., Magesh, N. and Prameela, V., Coefficient bounds for certain subclasses of bi-univalent functions, Abs. Appl. Anal., Volume 2013, Article ID 573017, 1-3.
  • Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Ration. Mech. Anal, 32, (1969), 100-112.
  • Olatunji, S.O. and Ajai, P.T., On subclasses of bi-univalent functions of Bazilevic type involving linear and Salagean operator, Internat. J. Pure Appl. Math. 92 no.5, (2014), 645-656,
  • Owa, S., Sekine, T., Yamakawa, R., On Sakaguchi type functions. Applied Mathematics and Computation, 187 (2007): 356-361.
  • Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan, 11(1), (1959), 72-75.
  • Shamugham, T.W., Ramachandran, C. and Ravichandran, V., Fetete-Szego Problem for a subclasses of starlike function with respect to symmetric points, Bull. Korean Math. Soc. 43(3) (2006), 589-598.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188--1192.
  • Taha, T.S., Topics in Univalent F unction Theory, Ph.D. Thesis, University of London, 1981
  • Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990--994.
  • Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012).
  • Zireh, A., Adegani, E.A. and Bulut, S., Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 487-504.

Year 2019, Volume: 68 Issue: 1, 724 - 733, 01.02.2019

Emeka Mazı Sahsene Altınkaya

https://doi.org/10.31801/cfsuasmas.464191
Cited By: 1

Abstract

References

  • Altınkaya, Ş. and Yalçın, S., On a new sublass of bi-univalent functions of Sakaguchi type satisfying subordinate condition, Malaya J. Mat. 5(2), 2017, 305-309.
  • Altınkaya, Ş. and Yalçın, S., Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 6 (2015), 180--185.
  • Altınkaya, Ş. and Yalçın, S., Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015 (2015), Article ID 145242, 1--5.
  • Altınkaya, Ş. and Yalçın, S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris Sér. I 353 (2015), 1075--1080.
  • Ali, R.M., Lee, S.K., Ravichandran, V. and Supramaniam, S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions. Appl. Math. Lett. 25, (2012) 344-351.
  • Babalola, K.O., On λ-pseudo-starlike functions, J. Class. Anal. 3(2), (2013) 137-147.
  • Brannan, D.A. and Clunie, J.G.(Eds.), Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979), Academic Press, New York and London, 1980.
  • Brannan D.A. and Taha, T.S., On some classes of bi-univalent functions Studia Univ. Babe¸s-Bolyai Math, 31(2), (1986).70-77.
  • Duren, P.L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York Berlin Heidelberg and Tokyo, 1983.
  • Frasin, B.A., Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci., 10(2) (2010), 206-211.
  • Goyal, S.P. and Goswami, P., Certain coefficient inequalities for Sakaguchi type functions and applications to fractional derivative operator, Acta Unisarsities Apulensis (No. 1912009)
  • Joshi, S. and Pawar, H., On some subclasses of bi-univalent functions associated with pseudo-starlike functions, Journal of the Egyptian Mathematical Society, 24, (2016), 522-525.
  • Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris Sér. I 354 (2016), 365--370.
  • Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc,18, (1967), 63-68.
  • Murugusundaramoorthy, G., Magesh, N. and Prameela, V., Coefficient bounds for certain subclasses of bi-univalent functions, Abs. Appl. Anal., Volume 2013, Article ID 573017, 1-3.
  • Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Ration. Mech. Anal, 32, (1969), 100-112.
  • Olatunji, S.O. and Ajai, P.T., On subclasses of bi-univalent functions of Bazilevic type involving linear and Salagean operator, Internat. J. Pure Appl. Math. 92 no.5, (2014), 645-656,
  • Owa, S., Sekine, T., Yamakawa, R., On Sakaguchi type functions. Applied Mathematics and Computation, 187 (2007): 356-361.
  • Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan, 11(1), (1959), 72-75.
  • Shamugham, T.W., Ramachandran, C. and Ravichandran, V., Fetete-Szego Problem for a subclasses of starlike function with respect to symmetric points, Bull. Korean Math. Soc. 43(3) (2006), 589-598.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188--1192.
  • Taha, T.S., Topics in Univalent F unction Theory, Ph.D. Thesis, University of London, 1981
  • Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990--994.
  • Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012).
  • Zireh, A., Adegani, E.A. and Bulut, S., Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 487-504.
There are 25 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Emeka Mazı 0000-0003-1748-6724

Sahsene Altınkaya 0000-0002-7950-8450

Publication Date February 1, 2019
Submission Date October 13, 2017
Acceptance Date April 2, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Mazı, E., & Altınkaya, S. (2019). On a new subclass of bi-univalent functions satisfying subordinate conditions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 724-733. https://doi.org/10.31801/cfsuasmas.464191
AMA Mazı E, Altınkaya S. On a new subclass of bi-univalent functions satisfying subordinate conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):724-733. doi:10.31801/cfsuasmas.464191
Chicago Mazı, Emeka, and Sahsene Altınkaya. “On a New Subclass of Bi-Univalent Functions Satisfying Subordinate Conditions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 724-33. https://doi.org/10.31801/cfsuasmas.464191.
EndNote Mazı E, Altınkaya S (February 1, 2019) On a new subclass of bi-univalent functions satisfying subordinate conditions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 724–733.
IEEE E. Mazı and S. Altınkaya, “On a new subclass of bi-univalent functions satisfying subordinate conditions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 724–733, 2019, doi: 10.31801/cfsuasmas.464191.
ISNAD Mazı, Emeka - Altınkaya, Sahsene. “On a New Subclass of Bi-Univalent Functions Satisfying Subordinate Conditions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 724-733. https://doi.org/10.31801/cfsuasmas.464191.
JAMA Mazı E, Altınkaya S. On a new subclass of bi-univalent functions satisfying subordinate conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:724–733.
MLA Mazı, Emeka and Sahsene Altınkaya. “On a New Subclass of Bi-Univalent Functions Satisfying Subordinate Conditions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 724-33, doi:10.31801/cfsuasmas.464191.
Vancouver Mazı E, Altınkaya S. On a new subclass of bi-univalent functions satisfying subordinate conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):724-33.

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