On the Coefficent Bound Estimates and Fekete-Szegö Problem
Year 2023,
Volume: 12 Issue: 2, 337 - 343, 27.06.2023
Nizami Mustafa
,
Semra Korkmaz
Abstract
In this study, we introduce and examine a certain subclass of analytic functions in the open unit disk in the complex plane. Here, we give coefficient bound estimates and investigate the Fekete-Szegö problem for the introduced class. Some interesting special cases of the results obtained here are also discussed.
References
- [1] M. Buyankara, M. Çağlar, L.-I. Cotîrlă, “New subclasses of bi-univalent functions with respect to the symmetric points defined by bernoulli polynomials”, Axioms, vol.11, no.11, pp. 652-660, 2022.
- [2] D. A. Brannan and J. Clunie, “Aspects of Contemporary Complex Analysis”, Academic Press, London and New York, USA, 1980.
- [3] D. A. Brannan and T. S. Taha, “On Some Classes of Bi-univalent Functions”, Studia Univ. Babes-Bolyai Mathematics, vol. 31, pp.70-77, 1986.
- [4] Y. Cheng, R. Srivastava, J. L. Liu, “Applications of the q-derivative operator to new families of bi-univalent functions related to the Legendre Polynomials”, Axioms, vol. 11, no.11, pp. 595-607, 2022.
- [5] J. Dziok, “Classes of meromorphic harmonic functions defined by Sălăgean operator”, Revista de la Real Academia de Ciencias Exactas, Físicay Naturales. Serie A. Matemáticas, vol. 116, no.4, pp.1-16, 2022.
- [6] P. L. Duren, “Univalent Functions”, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New- York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983.
- [7] M. Fekete and G. Szegö, “Eine Bemerkung über ungerade schlichte funktionen”, Journal of the London Mathematical Society, vol.8, pp.85-89, 1993.
- [8] U. Grenander and G. Szegö, “Toeplitz form and their applications”, California Monographs in Mathematical Sciences, University California Press, Berkeley, 1958.
- [9] H.Ö. Güney, G.I. Oros, S. Owa, “An Application of Sălăgean operator concerning starlike functions”, Axioms, vol. 11, no.2, pp. 50-59, 2022.
- [10] M. Lewin, “On a coefficient problem for bi-univalent functions”, Proceedings of the American Mathematical Society, vol.18, pp.63-68, 1967.
- [11] S. Li, L. Ma, H. Tang, “On Janowski type p-harmonic functions associated with generalized Sălăgean operator”, AIMS Mathematics, vol. 6, no.1, pp.569-583, 2021.
- [12] N. Mustafa, “Fekete- Szegö problem for certain subclass of analytic and bi-univalent functions”, Journal of Scientific and Engineering Research, vol.4, no.8, pp.30-400, 2017.
- [13] N. Mustafa and M. C. Gündüz, “The Fekete-Szegö problem for certain class of analytic and univalent functions”, Journal of Scientific and Engineering Research, vol.6, no.5, pp.232-239, 2019.
- [14] N. Mustafa and G. Murugusundaramoorthy, “Second Hankel for mocanu type bi-starlike functions related to shell shaped region”, Turkish Journal of Mathematics, vol.45, pp.1270-1286, 2021.
- [15] E. Netanyahu, “The minimal distance of the image boundary from the origin and the second coefficient of a univalent function”, Archive for Rational Mechanics and Analysis, vol.32, pp.100-112, 1969.
- [16] G.I. Oros, L.-I. Cotîrlă, “Coefficient Estimates and the Fekete–Szegö problem for new classes of m-fold symmetric bi-univalent functions”, Mathematics, vol. 10, pp. 129-141, 2022. https://doi.org/10.3390/math10010129
- [17] Á.O. Páll-Szabó, G. I. Oros, “Coefficient related studies for new classes of bi-univalent functions”, Mathematics, vol. 8, no.7, pp. 1110-1123, 2020.
- [18] G. S. Sălăgean, “Subclasses of univalent functions”, Complex Analysis, vol.103, pp.362-372, 1983.
- [19] H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Certain sublcasses of analytic and bi-univalent functions”, Applied Mathematics Letters, vol.23, pp.1188-1192, 2010.
- [20] H. M. Srivastava, G. Murugusundaramoorthy, T. Bulboacă, “The second Hankel determinant for subclasses of bi-univalent functions associated with a nephroid domain”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Mathemáticas, vol. 116, no.4, 1-21, 2022.
- [21] P. Zaprawa, “On the Fekete-Szegö problem for the classes of bi-univalent functions”, Bulletin of the Belgain Mathematical Society, vol.21, pp.169-178, 2014.
- [22] Q. H. Xu, G. Xiao and H. M. Srivastava, “A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems”, Applied Mathematics and Computation, vol. 218, pp.11461-11465, 2012.
Year 2023,
Volume: 12 Issue: 2, 337 - 343, 27.06.2023
Nizami Mustafa
,
Semra Korkmaz
References
- [1] M. Buyankara, M. Çağlar, L.-I. Cotîrlă, “New subclasses of bi-univalent functions with respect to the symmetric points defined by bernoulli polynomials”, Axioms, vol.11, no.11, pp. 652-660, 2022.
- [2] D. A. Brannan and J. Clunie, “Aspects of Contemporary Complex Analysis”, Academic Press, London and New York, USA, 1980.
- [3] D. A. Brannan and T. S. Taha, “On Some Classes of Bi-univalent Functions”, Studia Univ. Babes-Bolyai Mathematics, vol. 31, pp.70-77, 1986.
- [4] Y. Cheng, R. Srivastava, J. L. Liu, “Applications of the q-derivative operator to new families of bi-univalent functions related to the Legendre Polynomials”, Axioms, vol. 11, no.11, pp. 595-607, 2022.
- [5] J. Dziok, “Classes of meromorphic harmonic functions defined by Sălăgean operator”, Revista de la Real Academia de Ciencias Exactas, Físicay Naturales. Serie A. Matemáticas, vol. 116, no.4, pp.1-16, 2022.
- [6] P. L. Duren, “Univalent Functions”, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New- York, Berlin, Heidelberg and Tokyo, Springer-Verlag, 1983.
- [7] M. Fekete and G. Szegö, “Eine Bemerkung über ungerade schlichte funktionen”, Journal of the London Mathematical Society, vol.8, pp.85-89, 1993.
- [8] U. Grenander and G. Szegö, “Toeplitz form and their applications”, California Monographs in Mathematical Sciences, University California Press, Berkeley, 1958.
- [9] H.Ö. Güney, G.I. Oros, S. Owa, “An Application of Sălăgean operator concerning starlike functions”, Axioms, vol. 11, no.2, pp. 50-59, 2022.
- [10] M. Lewin, “On a coefficient problem for bi-univalent functions”, Proceedings of the American Mathematical Society, vol.18, pp.63-68, 1967.
- [11] S. Li, L. Ma, H. Tang, “On Janowski type p-harmonic functions associated with generalized Sălăgean operator”, AIMS Mathematics, vol. 6, no.1, pp.569-583, 2021.
- [12] N. Mustafa, “Fekete- Szegö problem for certain subclass of analytic and bi-univalent functions”, Journal of Scientific and Engineering Research, vol.4, no.8, pp.30-400, 2017.
- [13] N. Mustafa and M. C. Gündüz, “The Fekete-Szegö problem for certain class of analytic and univalent functions”, Journal of Scientific and Engineering Research, vol.6, no.5, pp.232-239, 2019.
- [14] N. Mustafa and G. Murugusundaramoorthy, “Second Hankel for mocanu type bi-starlike functions related to shell shaped region”, Turkish Journal of Mathematics, vol.45, pp.1270-1286, 2021.
- [15] E. Netanyahu, “The minimal distance of the image boundary from the origin and the second coefficient of a univalent function”, Archive for Rational Mechanics and Analysis, vol.32, pp.100-112, 1969.
- [16] G.I. Oros, L.-I. Cotîrlă, “Coefficient Estimates and the Fekete–Szegö problem for new classes of m-fold symmetric bi-univalent functions”, Mathematics, vol. 10, pp. 129-141, 2022. https://doi.org/10.3390/math10010129
- [17] Á.O. Páll-Szabó, G. I. Oros, “Coefficient related studies for new classes of bi-univalent functions”, Mathematics, vol. 8, no.7, pp. 1110-1123, 2020.
- [18] G. S. Sălăgean, “Subclasses of univalent functions”, Complex Analysis, vol.103, pp.362-372, 1983.
- [19] H. M. Srivastava, A. K. Mishra and P. Gochhayat, “Certain sublcasses of analytic and bi-univalent functions”, Applied Mathematics Letters, vol.23, pp.1188-1192, 2010.
- [20] H. M. Srivastava, G. Murugusundaramoorthy, T. Bulboacă, “The second Hankel determinant for subclasses of bi-univalent functions associated with a nephroid domain”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Mathemáticas, vol. 116, no.4, 1-21, 2022.
- [21] P. Zaprawa, “On the Fekete-Szegö problem for the classes of bi-univalent functions”, Bulletin of the Belgain Mathematical Society, vol.21, pp.169-178, 2014.
- [22] Q. H. Xu, G. Xiao and H. M. Srivastava, “A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems”, Applied Mathematics and Computation, vol. 218, pp.11461-11465, 2012.