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ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS

Year 2017, Volume: 66 Issue: 2, 289 - 296, 01.08.2017
https://doi.org/10.1501/Commua1_0000000819

Abstract

In this work, considering bi-Bazilevic functions and using theFaber polynomials, we obtain coefficient expansions for functions in this class.In certain cases, our estimates improve some of those existing coefficient bounds

References

  • Airault, H., Symmetric sums associated to the factorization of Grunsky coe¢ cients, in Con- ference, Groups and Symmetries, Montreal, Canada, April 2007.
  • Airault, H., Remarks on Faber polynomials, Int. Math. Forum 3 (2008), 449-456.
  • Airault, H. and Bouali, H., Diğerential calculus on the Faber polynomials, Bulletin des Sci- ences Mathematiques 130 (2006), 179-222.
  • Airault, H. and Ren, J., An algebra of diğerential operators and generating functions on the set of univalent functions, Bulletin des Sciences Mathematiques 126 (2002), 343-367.
  • Altınkaya, ¸S. and Yalçın, S., Coe¢ cient Estimates for Two New Subclasses of Bi-univalent Functions with respect to Symmetric Points, Journal of Function Spaces Article ID 145242, (2015), 5 pp.
  • Altınkaya, ¸S. and Yalçın, S., Faber polynomial coe¢ cient bounds for a subclass of bi-univalent function, C. R. Acad. Sci. Paris, Ser. I 353 (2015), 1075-1080.
  • Bazilevic, I. E., On a case of integrability in quadratures of the Loewner-Kufarev equation, Matematicheskii Sbornik 37 (1955), 471-476.
  • Brannan, D. A. and Clunie, J., Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Instute Held at University of Durham, New York: Academic Press, 1979.
  • Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Studia Universi- tatis Babe¸s-Bolyai Mathematica 31 (1986), 70-77.
  • Bulut, S., Magesh N. and Balaji, V. K., Faber polynomial coe¢ cient estimates for certain subclasses of meromorphic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 353 (2015), 113-116.
  • Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 259, 1983.
  • Faber, G., Über polynomische entwickelungen, Math. Ann. 57 (1903), 1569-1573.
  • Frasin, B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573.
  • Grunsky, H., Koe¢ zientenbedingungen für schlicht abbildende meromorphe funktionen, Math. Zeit. 45 (1939), 29-61.
  • Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coe¢ cient estimates for analytic bi- close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 17–20.
  • Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coe¢ cients of bi-subordinate function, C. R. Acad. Sci. Paris, Ser. I 354 (2016), 365-370.
  • Lewin, M., On a coe¢ cient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68.
  • Magesh, N., Rosy, T. and Varma, S., Coe¢ cient estimate problem for a new subclass of bi-univalent functions, Journal of Complex Analysis, Volume 2013, Article ID: 474231, 3 pages.
  • Magesh, N. and Yamini, J., Coe¢ cient bounds for certain subclasses of bi-univalent functions, Int. Math. Forum, 8 (27) (2013), 1337-1344.
  • Netanyahu, E., The minimal distance of the image boundary from the origin and the second coe¢ cient of a univalent function in jzj < 1; Archive for Rational Mechanics and Analysis 32 (1969), 100-112.
  • Rosihan, M. A., Lee, S. K., Ravichandran, V. and Supramaniama, S., Coe¢ cient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (2012), 344–351. [22] Schiğer, M., A method of variation within the family of simple functions, Proc. London Math. Soc. 44 (1938), 432-449.
  • Schaeğer, A. C. and Spencer, D. C., The coe¢ cients of schlicht functions, Duke Math. J. 10 (1943), 611-635.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192.
  • Srivastava, H. M., Joshi, S. B., Joshi, S. S. and Pawar, H., Coe¢ cient estimates for certain subclasses of meromorphically bi-univalent functions, Palest. J. Math. 5 (Special Issue: 1) (2016), 250-258.
  • Zaprawa, P., On Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), 169-178.
  • Current address : ¸Sahsene Altınkaya: Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059 Bursa, Turkey.
  • E-mail address : sahsene@uludag.edu.tr
  • Current address : Sibel Yalçın: Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059 Bursa, Turkey.
  • E-mail address : syalcin@uludag.edu.tr
Year 2017, Volume: 66 Issue: 2, 289 - 296, 01.08.2017
https://doi.org/10.1501/Commua1_0000000819

Abstract

References

  • Airault, H., Symmetric sums associated to the factorization of Grunsky coe¢ cients, in Con- ference, Groups and Symmetries, Montreal, Canada, April 2007.
  • Airault, H., Remarks on Faber polynomials, Int. Math. Forum 3 (2008), 449-456.
  • Airault, H. and Bouali, H., Diğerential calculus on the Faber polynomials, Bulletin des Sci- ences Mathematiques 130 (2006), 179-222.
  • Airault, H. and Ren, J., An algebra of diğerential operators and generating functions on the set of univalent functions, Bulletin des Sciences Mathematiques 126 (2002), 343-367.
  • Altınkaya, ¸S. and Yalçın, S., Coe¢ cient Estimates for Two New Subclasses of Bi-univalent Functions with respect to Symmetric Points, Journal of Function Spaces Article ID 145242, (2015), 5 pp.
  • Altınkaya, ¸S. and Yalçın, S., Faber polynomial coe¢ cient bounds for a subclass of bi-univalent function, C. R. Acad. Sci. Paris, Ser. I 353 (2015), 1075-1080.
  • Bazilevic, I. E., On a case of integrability in quadratures of the Loewner-Kufarev equation, Matematicheskii Sbornik 37 (1955), 471-476.
  • Brannan, D. A. and Clunie, J., Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Instute Held at University of Durham, New York: Academic Press, 1979.
  • Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Studia Universi- tatis Babe¸s-Bolyai Mathematica 31 (1986), 70-77.
  • Bulut, S., Magesh N. and Balaji, V. K., Faber polynomial coe¢ cient estimates for certain subclasses of meromorphic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 353 (2015), 113-116.
  • Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 259, 1983.
  • Faber, G., Über polynomische entwickelungen, Math. Ann. 57 (1903), 1569-1573.
  • Frasin, B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573.
  • Grunsky, H., Koe¢ zientenbedingungen für schlicht abbildende meromorphe funktionen, Math. Zeit. 45 (1939), 29-61.
  • Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coe¢ cient estimates for analytic bi- close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 17–20.
  • Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coe¢ cients of bi-subordinate function, C. R. Acad. Sci. Paris, Ser. I 354 (2016), 365-370.
  • Lewin, M., On a coe¢ cient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68.
  • Magesh, N., Rosy, T. and Varma, S., Coe¢ cient estimate problem for a new subclass of bi-univalent functions, Journal of Complex Analysis, Volume 2013, Article ID: 474231, 3 pages.
  • Magesh, N. and Yamini, J., Coe¢ cient bounds for certain subclasses of bi-univalent functions, Int. Math. Forum, 8 (27) (2013), 1337-1344.
  • Netanyahu, E., The minimal distance of the image boundary from the origin and the second coe¢ cient of a univalent function in jzj < 1; Archive for Rational Mechanics and Analysis 32 (1969), 100-112.
  • Rosihan, M. A., Lee, S. K., Ravichandran, V. and Supramaniama, S., Coe¢ cient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (2012), 344–351. [22] Schiğer, M., A method of variation within the family of simple functions, Proc. London Math. Soc. 44 (1938), 432-449.
  • Schaeğer, A. C. and Spencer, D. C., The coe¢ cients of schlicht functions, Duke Math. J. 10 (1943), 611-635.
  • Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192.
  • Srivastava, H. M., Joshi, S. B., Joshi, S. S. and Pawar, H., Coe¢ cient estimates for certain subclasses of meromorphically bi-univalent functions, Palest. J. Math. 5 (Special Issue: 1) (2016), 250-258.
  • Zaprawa, P., On Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), 169-178.
  • Current address : ¸Sahsene Altınkaya: Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059 Bursa, Turkey.
  • E-mail address : sahsene@uludag.edu.tr
  • Current address : Sibel Yalçın: Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059 Bursa, Turkey.
  • E-mail address : syalcin@uludag.edu.tr
There are 29 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Şahsene Altınkaya This is me

Sibel Yalçın This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Altınkaya, Ş., & Yalçın, S. (2017). ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 289-296. https://doi.org/10.1501/Commua1_0000000819
AMA Altınkaya Ş, Yalçın S. ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):289-296. doi:10.1501/Commua1_0000000819
Chicago Altınkaya, Şahsene, and Sibel Yalçın. “ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 289-96. https://doi.org/10.1501/Commua1_0000000819.
EndNote Altınkaya Ş, Yalçın S (August 1, 2017) ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 289–296.
IEEE Ş. Altınkaya and S. Yalçın, “ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 289–296, 2017, doi: 10.1501/Commua1_0000000819.
ISNAD Altınkaya, Şahsene - Yalçın, Sibel. “ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 289-296. https://doi.org/10.1501/Commua1_0000000819.
JAMA Altınkaya Ş, Yalçın S. ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:289–296.
MLA Altınkaya, Şahsene and Sibel Yalçın. “ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 289-96, doi:10.1501/Commua1_0000000819.
Vancouver Altınkaya Ş, Yalçın S. ON THE FABER POLYNOMIAL COEFFICIENT BOUNDS OF BI-BAZILEVIC FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):289-96.

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

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