Coefficient Estimates for Subclass of m-Fold Symmetric Bi- Univalent Functions


Download PDF

Authors: A. MOTAMEDNEZHAD, S. SALEHIAN AND N. MAGESH

DOI: 10.46793/KgJMat2203.395M

Abstract:

In the present paper, a general subclass Σmh,p(λ,γ) of the m-Fold symmetric bi-univalent functions is defined. Also, the estimates of the Taylor-Maclaurin coefficients |am+1|, |a2m+1| and Fekete-Szegö problems are obtained for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.



Keywords:

Bi-univalent functions, m-fold symmetric univalent functions, m-fold symmetric bi-univalent functions, coefficient estimates, Fekete-Szegö problem.



References:

[1]   Ş. Altinkaya and S. Yalçin, Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions, J. Math.2015 (2015), Article ID 241683, 5 pages.

[2]   D. Breaz, N. Breaz and H. M. Sirvastava, An extention of the univalent conditions for a family of integral operators, Appl. Math. Lett. 22 (2009), 41–44.

[3]   P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg. Tokyo, 1983.

[4]   M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.

[5]   H. V. Smith, Bi-univalent polynomials, Simon Stevin 50(2) (1976/77), 115–122.

[6]   H. M. Srivastava, S. Bulut, M. Çağlar and N. Yağmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27(5) (2013), 831–842.

[7]   H. M. Srivastava, S. Gaboury and F. Ghanim, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Math. Sci. Ser. B 36(3) (2016), 863–871.

[8]   H. M. Srivastava, S. Gaboury and F. Ghanim, Coefficient estimates for some general subclasses of analytic and bi-univalent functions, Afr. Mat. 28 (2017), 693–706.

[9]   H. M. Srivastava, S. Gaboury and F. Ghanim, Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Univ. Apulensis Math. Inform. 41 (2015), 153–164.

[10]   H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192.

[11]   H. M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi Math. J. 7(2) (2014), 1–10.

[12]   H. M. Srivastava, A. Zireh and S. Hajiparvaneh, Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Filomat 32(9) (2018), 3143–3153.

[13]   X. -F. Li and A. -P. Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum 7(30) (2012), 1495–1504.

[14]   A. Zireh and S. Salehian, On the certain subclass of analytic and bi-univalent functions defined by convolution, Acta Univ. Apulensis Math. Inform. 44 (2015), 9–19.