2018/10/15 by Magesh, N., Balaji, V. K., Abirami, C.
#30C45 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1810.06216
Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al. \citeHMS-AKM-PG actually revived the study of the coefficient problems involving bi-univalent functions. Inspired by the pioneering work of Srivastava et al. \citeHMS-AKM-PG, there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Ali et al. \citeAli-Ravi-Ma-Mina-class, Srivastava et al. \citeHMS-AKM-PG and Güney et al. \citeHOG-GMS-JS-Fib-2018 in this paper, we consider certain classes of bi-univalent functions related to shell-like curves connected with Fibonacci numbers to obtain the estimates of second, third Taylor-Maclaurin coefficients and Fekete - Szegö inequalities. Further, certain special cases are also indicated. Some interesting remarks of the results presented here are also discussed.