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Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator

Year 2017, Volume: 66 Issue: 1, 85 - 91, 01.02.2017
https://doi.org/10.1501/Commua1_0000000777

References

  • R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coe¢ cient estimates for bi- univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344–351. [2] D. A. Brannan, J.G. Clunie (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.
  • D. A. Brannan and T.S. Taha, On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Math. Anal. and Appl., Kuwait; February 18–21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53–60. see also Studia Univ. Babe¸s-Bolyai Math. 31 (2) (1986), 70–77.
  • S. Bulut, Faber polynomial coe¢ cient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 352 (6) (2014), pp. 479–484.
  • S. Bulut, N. Magesh and V. K. Balaji, Faber polynomial coe¢ cient estimates for certain subclasses of meromorphic bi-univalent functions, Comptes Rendus Mathematique 353(2) (2015), 113-116.
  • M. Ça¼glar, H. Orhan and N. Ya¼gmur, Coe¢ cient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013), 1165-1171.
  • E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2(1) (2013), 49–60.
  • P. L. Duren, Univalent functions,Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, 1983.
  • B. A. Frasin, M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573.
  • S. G. Hamidi, J. M. Jahangiri, Faber polynomial coe¢ cient estimates for analytic bi-close- to-convex functions, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 17–20.
  • A. W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ.Mariae Curie- Skğodowska Sect. A 39 (1985), 77–81 (1988).
  • S. Sivaprasad Kumar, V. Kumar and V. Ravichandran, Estimates for the initial coe¢ cients of bi-univalent functions, Tamsui Oxford J. Inform. Math. Sci. 29(4) (2013), 487-504.
  • M. Lewin, On a coe¢ cient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.
  • A. K. Mishra and S. Barık, Estimates for the initial coe¢ cients of bi-univalent
  • convex analytic functions in the unit disc, Journal of Classical Analysis, 7(1) (2015), 73-81.
  • E. Netanyahu, The minimal distance of the image boundary from the origin and the second coe¢ cient of a univalent function in jzj < 1, Arch. Rational Mech. Anal. 32 (1969), 100-112. [16] H. Orhan, N. Magesh and V. K. Balaji, Initial coe¢ cient bounds for a general class of bi- univalent functions, Filomat 29(6) (2015), 1259–1267.
  • C. Ramachandran, R. Ambrose Prabhu and N. Magesh, Initial coe¢ cient estimates for certain subclasses of bi-univalent functions of Ma-Minda type, Applied Mathematical Sciences, 9(47) (2015), 2299-2308.
  • G. S. Salagean, Subclasses of univalent functions, Complex analysis - Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math., 1013 (1983), 362–372.
  • H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192.
  • H. M. Srivastava, S. Bulut, M. Ça¼glar, N. Ya¼gmur, Coe¢ cient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27(5) (2013), 831-842.
  • H. M. Srivastava and D. Bansal, Coe¢ cient estimates for a subclass of analytic and bi- univalent functions, Journal of the Egyptian Mathematical Society 23(2) (2015), 242-246.
  • Y. Sun, Y. P. Jiang and A. Rasila, Coe¢ cient estimates for certain subclasses of analytic and bi-univalent functions, Filomat 29(2) (2015), 351-360.
  • D. L. Tan, Coe¢ cient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A 5 (5) (1984), 559–568.
  • P. Zaprawa, Estimates of initial coe¢ cients for bi-univalent functions, Abstr. Appl. Anal., 2014, Article ID 357480, 6 pages.
Year 2017, Volume: 66 Issue: 1, 85 - 91, 01.02.2017
https://doi.org/10.1501/Commua1_0000000777

References

  • R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coe¢ cient estimates for bi- univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344–351. [2] D. A. Brannan, J.G. Clunie (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.
  • D. A. Brannan and T.S. Taha, On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Math. Anal. and Appl., Kuwait; February 18–21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53–60. see also Studia Univ. Babe¸s-Bolyai Math. 31 (2) (1986), 70–77.
  • S. Bulut, Faber polynomial coe¢ cient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 352 (6) (2014), pp. 479–484.
  • S. Bulut, N. Magesh and V. K. Balaji, Faber polynomial coe¢ cient estimates for certain subclasses of meromorphic bi-univalent functions, Comptes Rendus Mathematique 353(2) (2015), 113-116.
  • M. Ça¼glar, H. Orhan and N. Ya¼gmur, Coe¢ cient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013), 1165-1171.
  • E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2(1) (2013), 49–60.
  • P. L. Duren, Univalent functions,Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, 1983.
  • B. A. Frasin, M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573.
  • S. G. Hamidi, J. M. Jahangiri, Faber polynomial coe¢ cient estimates for analytic bi-close- to-convex functions, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 17–20.
  • A. W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ.Mariae Curie- Skğodowska Sect. A 39 (1985), 77–81 (1988).
  • S. Sivaprasad Kumar, V. Kumar and V. Ravichandran, Estimates for the initial coe¢ cients of bi-univalent functions, Tamsui Oxford J. Inform. Math. Sci. 29(4) (2013), 487-504.
  • M. Lewin, On a coe¢ cient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.
  • A. K. Mishra and S. Barık, Estimates for the initial coe¢ cients of bi-univalent
  • convex analytic functions in the unit disc, Journal of Classical Analysis, 7(1) (2015), 73-81.
  • E. Netanyahu, The minimal distance of the image boundary from the origin and the second coe¢ cient of a univalent function in jzj < 1, Arch. Rational Mech. Anal. 32 (1969), 100-112. [16] H. Orhan, N. Magesh and V. K. Balaji, Initial coe¢ cient bounds for a general class of bi- univalent functions, Filomat 29(6) (2015), 1259–1267.
  • C. Ramachandran, R. Ambrose Prabhu and N. Magesh, Initial coe¢ cient estimates for certain subclasses of bi-univalent functions of Ma-Minda type, Applied Mathematical Sciences, 9(47) (2015), 2299-2308.
  • G. S. Salagean, Subclasses of univalent functions, Complex analysis - Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math., 1013 (1983), 362–372.
  • H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192.
  • H. M. Srivastava, S. Bulut, M. Ça¼glar, N. Ya¼gmur, Coe¢ cient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27(5) (2013), 831-842.
  • H. M. Srivastava and D. Bansal, Coe¢ cient estimates for a subclass of analytic and bi- univalent functions, Journal of the Egyptian Mathematical Society 23(2) (2015), 242-246.
  • Y. Sun, Y. P. Jiang and A. Rasila, Coe¢ cient estimates for certain subclasses of analytic and bi-univalent functions, Filomat 29(2) (2015), 351-360.
  • D. L. Tan, Coe¢ cient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A 5 (5) (1984), 559–568.
  • P. Zaprawa, Estimates of initial coe¢ cients for bi-univalent functions, Abstr. Appl. Anal., 2014, Article ID 357480, 6 pages.
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Murat Çağlar This is me

Erhan Denız This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 1

Cite

APA Çağlar, M., & Denız, E. (2017). Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 85-91. https://doi.org/10.1501/Commua1_0000000777
AMA Çağlar M, Denız E. Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):85-91. doi:10.1501/Commua1_0000000777
Chicago Çağlar, Murat, and Erhan Denız. “Initial Coefficients for a Subclass of Bi-Univalent Functions Defined by Salagean Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 85-91. https://doi.org/10.1501/Commua1_0000000777.
EndNote Çağlar M, Denız E (February 1, 2017) Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 85–91.
IEEE M. Çağlar and E. Denız, “Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 85–91, 2017, doi: 10.1501/Commua1_0000000777.
ISNAD Çağlar, Murat - Denız, Erhan. “Initial Coefficients for a Subclass of Bi-Univalent Functions Defined by Salagean Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 85-91. https://doi.org/10.1501/Commua1_0000000777.
JAMA Çağlar M, Denız E. Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:85–91.
MLA Çağlar, Murat and Erhan Denız. “Initial Coefficients for a Subclass of Bi-Univalent Functions Defined by Salagean Differential Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 85-91, doi:10.1501/Commua1_0000000777.
Vancouver Çağlar M, Denız E. Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):85-91.

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