Analitik Fonksiyonların Belirli Bir Sınıfı İçin Fekete-Szegö Problemi Üzerine

Yıl 2022, Cilt: 15 Sayı: 2, 72 - 76, 31.03.2023

Nizami Mustafa , Semra Korkmaz

https://doi.org/10.58688/kujs.1233710

Öz

Bu çalışmada, kompleks düzlemin açık birim diskinde analitik fonksiyonların belirli bir alt sınıfı tanıtılıyor ve inceleniyor. Sonrasında tanıtılan sınıf için katsayı sınır tahminleri verilir ve Fekete-Szegö problemi incelenir. Ayrıca, bulunan sonuçların bazı ilginç özel durumları tartışılır.

Anahtar Kelimeler

Katsayı tahminleri, Fekete-Szegö problemi, Analitik fonksiyon

The Fekete-Szegö Problem for a Certain class of Analytic Functions

Öz

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 this class. Some interesting special cases of the results obtained here are also discussed.

Anahtar Kelimeler

Coefficient estimates, Fekete-Szegö problem, Analytic function

Kaynakça

• Buyankara M., Çağlar M., Cotîrlă L.-I. (2022.) New subclasses of bi-univalent functions with respect to the symmetric points defined by Bernoulli polynomials. Axioms. 11(11), 652-660.
• 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.
• Cheng Y., Srivastava R., Liu J. L. (2022). Applications of the q-derivative operator to new families of bi-univalent functions related to the Legendre Polynomials. Axioms. 11(11), 595-607.
• 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 Research, 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.
• Oros G.I., Cotîrlă L.-I. (2022). Coefficient Estimates and the Fekete–Szegö problem for new classes of m-fold symmetric bi-univalent functions. Mathematics, 10, 129-141.
• Srivastava H.M., Mishra A.K. and Gochhayat P. (2010). Certain subclasses of analytic and bi-univalent functions. Applied Mathematics Letters, 23, 1188-1192.
• Srivastava H. M., Murugusundaramoorthy G., Bulboacă T. (2022). The second Hankel determinant for subclasses of bi-univalent functions is associated with a nephroid domain. Revista de la Real Academia de Ciencias Exactas, Físicasy Naturales. Serie A. Mathemáticas, 116(4), 1-21.
• Zaprawa P. (2014). On the Fekete- Szegö Problem for the Classes of Bi-Univalent Functions. Bulletin of the Belgian Mathematical Society, 21, 169-178.