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Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions

Year 2019, Volume: 68 Issue: 2, 1401 - 1410, 01.08.2019
https://doi.org/10.31801/cfsuasmas.530879

Abstract

Considering a new subclass of m-fold symmetric analytic bi-univalent functions, we determine estimates the coefficient bounds for the Taylor-Maclaurin coefficients |a_{m+1}| and |a_{2m+1}| of the functions in this class. In certain cases, our estimates improve some of those existing coeffcient bounds.

References

  • Altınkaya, Ş. and Yalçın, S., Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions, J. Math. (2015), Art. ID 241683, 5 pp.
  • Atshan, W.G. and Al-Ziadi, N.A.J., Coefficients bounds for a general subclasses of m-fold symmetric bi-univalent functions, J. Al-Qadisiyah Comput. Sci. Math. 9 (2) (2017), 33--39.
  • Brannan, D.A. and Taha, T.S., On some classes of bi-univalent functions, in Mathematical Analysis and Its Applications (S. M. Mazhar, A. Hamoui and N. S. Faour, Editors) (Kuwait; February 18--21, 1985), KFAS Proceedings Series, Vol. 3, Pergamon Press (Elsevier Science Limited), Oxford, 1988, pp. 53--60; see also Studia Univ. Babes¸-Bolyai Math. 31 (2) (1986), 70--77.
  • Bulut, S., Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions, Turkish J. Math. 40 (6) (2016), 1386--1397.
  • Bulut, S., Magesh, N. and Balaji, V.K., Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 353 (2015), 113--116.
  • Frasin, B.A. and Aouf, M.K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011) 1569--1573.
  • Hamidi, S.G. and Jahangiri, J.M., Unpredictability of the coefficients of m-fold symmetric bi-starlike functions, Internat. J. Math. 25 (7) (2014), 1450064, 8 pp.
  • Pommerenke, Ch., On the coefficients of close-to-convex functions, Michigan. Math. J. 9 (1962), 259--269.
  • Ramachandran, C., Prabhu, Ambrose R. and Magesh, N., Initial coefficient estimates for certain subclasses of bi-univalent functions of Ma-Minda type, Applied Mathematical Sciences 9 (47) (2015), 2299--2308.
  • Srivastava, H.M., Bulut, S., Çağlar, M. and Yağmur, N., Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27 (5) (2013), 831--842.
  • Srivastava, H.M., Gaboury, S. and Ghanim, F., Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Univ. Apulensis Math. Inform. 41 (2015), 153--164. Srivastava, H.M., Gaboury, S. and Ghanim, F., Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed. 36 (3) (2016), 863--871.
  • Srivastava, H.M., Murugusundaramoorthy, G. and Magesh, N., On certain subclasses of bi-univalent functions associated with Hohlov operator, Global Journal of Mathematical Analysis 1 (2) (2013), 67--73.
  • Srivastava, H.M., Sivasubramanian, S. and Sivakumar, R., Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 7 (2) (2014), 1--10.
  • Srivastava, H.M., Mishra, A.K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188--1192.
  • Sümer Eker, S., Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turkish J. Math. 40 (3) (2016), 641--646.
  • Tang, H., Srivastava, H.M., Sivasubramanian, S. and Gurusamy, P., The Fekete-Szegö functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal. 10 (4) (2016), 1063--1092.
  • 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) 11461--11465.
Year 2019, Volume: 68 Issue: 2, 1401 - 1410, 01.08.2019
https://doi.org/10.31801/cfsuasmas.530879

Abstract

References

  • Altınkaya, Ş. and Yalçın, S., Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions, J. Math. (2015), Art. ID 241683, 5 pp.
  • Atshan, W.G. and Al-Ziadi, N.A.J., Coefficients bounds for a general subclasses of m-fold symmetric bi-univalent functions, J. Al-Qadisiyah Comput. Sci. Math. 9 (2) (2017), 33--39.
  • Brannan, D.A. and Taha, T.S., On some classes of bi-univalent functions, in Mathematical Analysis and Its Applications (S. M. Mazhar, A. Hamoui and N. S. Faour, Editors) (Kuwait; February 18--21, 1985), KFAS Proceedings Series, Vol. 3, Pergamon Press (Elsevier Science Limited), Oxford, 1988, pp. 53--60; see also Studia Univ. Babes¸-Bolyai Math. 31 (2) (1986), 70--77.
  • Bulut, S., Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions, Turkish J. Math. 40 (6) (2016), 1386--1397.
  • Bulut, S., Magesh, N. and Balaji, V.K., Faber polynomial coefficient estimates for certain subclasses of meromorphic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 353 (2015), 113--116.
  • Frasin, B.A. and Aouf, M.K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011) 1569--1573.
  • Hamidi, S.G. and Jahangiri, J.M., Unpredictability of the coefficients of m-fold symmetric bi-starlike functions, Internat. J. Math. 25 (7) (2014), 1450064, 8 pp.
  • Pommerenke, Ch., On the coefficients of close-to-convex functions, Michigan. Math. J. 9 (1962), 259--269.
  • Ramachandran, C., Prabhu, Ambrose R. and Magesh, N., Initial coefficient estimates for certain subclasses of bi-univalent functions of Ma-Minda type, Applied Mathematical Sciences 9 (47) (2015), 2299--2308.
  • Srivastava, H.M., Bulut, S., Çağlar, M. and Yağmur, N., Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27 (5) (2013), 831--842.
  • Srivastava, H.M., Gaboury, S. and Ghanim, F., Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Univ. Apulensis Math. Inform. 41 (2015), 153--164. Srivastava, H.M., Gaboury, S. and Ghanim, F., Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed. 36 (3) (2016), 863--871.
  • Srivastava, H.M., Murugusundaramoorthy, G. and Magesh, N., On certain subclasses of bi-univalent functions associated with Hohlov operator, Global Journal of Mathematical Analysis 1 (2) (2013), 67--73.
  • Srivastava, H.M., Sivasubramanian, S. and Sivakumar, R., Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 7 (2) (2014), 1--10.
  • Srivastava, H.M., Mishra, A.K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188--1192.
  • Sümer Eker, S., Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turkish J. Math. 40 (3) (2016), 641--646.
  • Tang, H., Srivastava, H.M., Sivasubramanian, S. and Gurusamy, P., The Fekete-Szegö functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Inequal. 10 (4) (2016), 1063--1092.
  • 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) 11461--11465.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Serap Bulut 0000-0002-6506-4588

Publication Date August 1, 2019
Submission Date November 15, 2017
Acceptance Date September 9, 208
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Bulut, S. (2019). Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1401-1410. https://doi.org/10.31801/cfsuasmas.530879
AMA Bulut S. Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1401-1410. doi:10.31801/cfsuasmas.530879
Chicago Bulut, Serap. “Coefficient Estimates for a New Subclass of M-Fold Symmetric Analytic Bi-Univalent Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1401-10. https://doi.org/10.31801/cfsuasmas.530879.
EndNote Bulut S (August 1, 2019) Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1401–1410.
IEEE S. Bulut, “Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1401–1410, 2019, doi: 10.31801/cfsuasmas.530879.
ISNAD Bulut, Serap. “Coefficient Estimates for a New Subclass of M-Fold Symmetric Analytic Bi-Univalent Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1401-1410. https://doi.org/10.31801/cfsuasmas.530879.
JAMA Bulut S. Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1401–1410.
MLA Bulut, Serap. “Coefficient Estimates for a New Subclass of M-Fold Symmetric Analytic Bi-Univalent Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1401-10, doi:10.31801/cfsuasmas.530879.
Vancouver Bulut S. Coefficient estimates for a new subclass of m-fold symmetric analytic bi-univalent functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1401-10.

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

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