Certain classes of bi-univalent functions related to Shell-like curves connected with Fibonacci numbers
Abstract
Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al. HMS-AKM-PG actually revived the study of the coefficient problems involving bi-univalent functions. Inspired by the pioneering work of Srivastava et al. HMS-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. Ali-Ravi-Ma-Mina-class, Srivastava et al. HMS-AKM-PG and G\"uney et al. HOG-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 - Szeg\"o inequalities. Further, certain special cases are also indicated. Some interesting remarks of the results presented here are also discussed.
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