Initial estimates for certain subclasses of bi-univalent functions with $\kappa-$Fibonacci numbers

Abstract

In this work, we consider certain class of bi-univalent functions related with shell-like curves related to $\kappa-$Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third coefficients) and Fekete - Szeg\"{o} inequalities. Also we discuss the special cases of the obtained results.