On the Coefficiend Bound Estimates and Fekete-Szegö Problem for a Certain Class of Analytic Functions

Yıl 2021, Cilt 14, Sayı 1 - 2, 1 - 8, 26.10.2022

Nizami MUSTAFA Semra KORKMAZ Zeynep GÖKKUŞ

Öz

In this study, we introduce and examine a certain subclass of analytic and 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.

Anahtar Kelimeler

Fekete-Szegö problemi, tek değerli fonksiyon, Salagean operatörü

Kaynakça

• 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. (1983). Eine Bemerkung Über Ungerade Schlichte Funktionen. Journal of the London Mathematical Society, 8, 85-89.
• 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 Research, 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.