Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator

Yıl 2019, Cilt: 2 Sayı: 1, 9 - 12, 30.10.2019

Fethiye Müge Sakar , Seher Melike Aydoğan Şahsene Altınkaya

Öz

In this study, we construct a new subclass of $m$-fold symmetric bi-univalent functions using by Hadamard product and generalized Salagean differential operator in the open unit disk $U=\left\{ z\in \mathbb{C} :\left\vert z\right\vert <1\right\} $. We establish upper bounds for the coefficients $\left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert $ belonging to this new class. The results presented here generalize some of the earlier studies.

Anahtar Kelimeler

Coefficient estimates, bi-univalent functions, m-fold symmetric functions

Destekleyen Kurum

Batman University

Proje Numarası

BTUBAP2018-IIBF-2

Kaynakça

• [1] F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci., 27 (2004), 1429-1436.
• [2] D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babe¸s-Bolyai Mathematica, 31 (1986), 70-77.
• [3] S. Bulut, Coefficient estimates for general subclasses ofm-fold symmetric analytic bi-univalent functions, Turkish J. Math., 40 (2016), 1386-1397.
• [4] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA 259, 1983.
• [5] S. G. Hamidi, J. M. Jahangiri, Unpredictability of the coefficients ofm-fold symmetric bi-starlike functions, Internat. J. Math., 25 (2014), 1-8.
• [6] M. Lewin, On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society, 18 (1967), 63-68.
• [7] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
• [8] Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Gottingen, 1975.
• [9] G. S. Salagean, Subclasses of univalent functions, in Complex Analysis, Fifth Romanian Finish Seminar, Part 1 (Bucharest, 1981), 1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983.
• [10] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters, 23 (2010), 1188-1192.
• [11] H. M. Srivastava, S. Sivasubramanian, R. Sivakumar, Initial coefficient bounds for a subclass ofm-fold symmetric bi-univalent functions, Tbilisi Mathematical Journal, 7 (2014), 1-10.
• [12] S. Sumer Eker, Coefficient bounds for subclasses ofm-fold symmetric bi-univalent functions, Turkish J. Math., 40 (2016), 641-646.