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Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions

Year 2022, Volume: 7 Issue: 3, 211 - 218, 30.12.2022

Abstract

In this study, we introduce and examine a certain subclass of analytic and bi-univalent functions in the open unit disk in the complex plane. Here, we give coefficient bound estimates and examine the Fekete-Szegö problem for this class. Some interesting special cases of the results obtained here are also discussed.

References

  • Brannan, D.A. and Clunie, J. (1980). Aspects of contemporary complex analysis. Academic Press, London and New York, USA.
  • Brannan, D.A. and Taha, T.S. (1986). On some classes of bi-univalent functions. Studia Univ. Babes-Bolyai Mathematics, 31, 70-77.
  • Duren, P.L. (1983). Univalent Functions. In: Grundlehren der Mathematischen Wissenschaften, Band 259, New- York, Berlin, Heidelberg and Tokyo, Springer- Verlag.
  • Grenander, U. and Szegö, G. (1958). Toeplitz Form and Their Applications. California Monographs in Mathematical Sciences, University California Press, Berkeley.
  • Fekete, M. and Szegö, G. (1993). Eine Bemerkung Über Ungerade Schlichte Funktionen. Journal of the London Mathematical Society, 8, 85-89.
  • Jackson, F.H. (1910). On -Definite Integrals. The Quarterly Journal of Pure and Apllied Mathematics, 41, 193-203.
  • Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American Mathematical Society, 18, 63-68.
  • Mustafa, N. (2017). Fekete- Szegö Problem for Certain Subclass of Analytic and Bi- Univalent Functions. Journal of Scientific and Engineering Reserch, 4(8), 30-400.
  • Mustafa, N. and Gündüz, M.C. (2019) The Fekete-Szegö Problem for Certain Class of Analytic and Univalent Functions. Journal of Scientific and Engineering Reserch, 6(5), 232-239.
  • Mustafa, N. and Mrugusundaramoorthy, G. (2021). Second Hankel for Mocanu Type Bi-Starlike Functions Related to Shell Shaped Region. Turkish Journal of Mathematics, 45, 1270-1286.
  • Netanyahu, E. (1969). The minimal distance of the image boundary from the origin and the second coefficient of a univalent function. Archive for Rational Mechanics and Analysis, 32, 100-112.
  • Salagean, G.S. (1983). Subclasses of Univalent Functions. Complex Analysis, 103, 362-372.
  • Srivastava, H.M., Mishra, A.K. and Gochhayat, P. (2010). Certain sublcasses of analytic and bi-univalent functions. Applied Mathematics Letters, 23, 1188-1192.
  • Zaprawa, P. (2014). On the Fekete- Szegö Problem for the Classes of Bi-Univalent Functions. Bulletin of the Belgain Mathematical Society, 21, 169-178.
  • Xu, Q.H., Xiao, G. and Srivastava, H.M. (2012). A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems. Applied Mathematics and Computation, 218, 11461-11465.
Year 2022, Volume: 7 Issue: 3, 211 - 218, 30.12.2022

Abstract

References

  • Brannan, D.A. and Clunie, J. (1980). Aspects of contemporary complex analysis. Academic Press, London and New York, USA.
  • Brannan, D.A. and Taha, T.S. (1986). On some classes of bi-univalent functions. Studia Univ. Babes-Bolyai Mathematics, 31, 70-77.
  • Duren, P.L. (1983). Univalent Functions. In: Grundlehren der Mathematischen Wissenschaften, Band 259, New- York, Berlin, Heidelberg and Tokyo, Springer- Verlag.
  • Grenander, U. and Szegö, G. (1958). Toeplitz Form and Their Applications. California Monographs in Mathematical Sciences, University California Press, Berkeley.
  • Fekete, M. and Szegö, G. (1993). Eine Bemerkung Über Ungerade Schlichte Funktionen. Journal of the London Mathematical Society, 8, 85-89.
  • Jackson, F.H. (1910). On -Definite Integrals. The Quarterly Journal of Pure and Apllied Mathematics, 41, 193-203.
  • Lewin, M. (1967). On a coefficient problem for bi-univalent functions. Proceedings of the American Mathematical Society, 18, 63-68.
  • Mustafa, N. (2017). Fekete- Szegö Problem for Certain Subclass of Analytic and Bi- Univalent Functions. Journal of Scientific and Engineering Reserch, 4(8), 30-400.
  • Mustafa, N. and Gündüz, M.C. (2019) The Fekete-Szegö Problem for Certain Class of Analytic and Univalent Functions. Journal of Scientific and Engineering Reserch, 6(5), 232-239.
  • Mustafa, N. and Mrugusundaramoorthy, G. (2021). Second Hankel for Mocanu Type Bi-Starlike Functions Related to Shell Shaped Region. Turkish Journal of Mathematics, 45, 1270-1286.
  • Netanyahu, E. (1969). The minimal distance of the image boundary from the origin and the second coefficient of a univalent function. Archive for Rational Mechanics and Analysis, 32, 100-112.
  • Salagean, G.S. (1983). Subclasses of Univalent Functions. Complex Analysis, 103, 362-372.
  • Srivastava, H.M., Mishra, A.K. and Gochhayat, P. (2010). Certain sublcasses of analytic and bi-univalent functions. Applied Mathematics Letters, 23, 1188-1192.
  • Zaprawa, P. (2014). On the Fekete- Szegö Problem for the Classes of Bi-Univalent Functions. Bulletin of the Belgain Mathematical Society, 21, 169-178.
  • Xu, Q.H., Xiao, G. and Srivastava, H.M. (2012). A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems. Applied Mathematics and Computation, 218, 11461-11465.
There are 15 citations in total.

Details

Primary Language English
Journal Section Volume VII Issue III
Authors

Nizami Mustafa 0000-0002-2758-0274

Semra Korkmaz 0000-0002-7846-9779

Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 7 Issue: 3

Cite

APA Mustafa, N., & Korkmaz, S. (2022). Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions. Turkish Journal of Science, 7(3), 211-218.
AMA Mustafa N, Korkmaz S. Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions. TJOS. December 2022;7(3):211-218.
Chicago Mustafa, Nizami, and Semra Korkmaz. “Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-Univalent Functions”. Turkish Journal of Science 7, no. 3 (December 2022): 211-18.
EndNote Mustafa N, Korkmaz S (December 1, 2022) Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions. Turkish Journal of Science 7 3 211–218.
IEEE N. Mustafa and S. Korkmaz, “Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions”, TJOS, vol. 7, no. 3, pp. 211–218, 2022.
ISNAD Mustafa, Nizami - Korkmaz, Semra. “Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-Univalent Functions”. Turkish Journal of Science 7/3 (December 2022), 211-218.
JAMA Mustafa N, Korkmaz S. Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions. TJOS. 2022;7:211–218.
MLA Mustafa, Nizami and Semra Korkmaz. “Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-Univalent Functions”. Turkish Journal of Science, vol. 7, no. 3, 2022, pp. 211-8.
Vancouver Mustafa N, Korkmaz S. Coefficient Bound Estimates and Fekete-Szegö Problem for a Certain Subclass of Analytic and Bi-univalent Functions. TJOS. 2022;7(3):211-8.