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

TL;DR

This paper investigates bi-univalent functions connected with shell-like curves and $6kappa$-Fibonacci numbers, providing coefficient estimates and inequalities, with special case discussions.

Contribution

It introduces new subclasses of bi-univalent functions linked to $6kappa$-Fibonacci numbers and derives initial coefficient bounds and inequalities.

Findings

Estimates for second and third Taylor-Maclaurin coefficients

Fekete-Szeg"o inequalities for the class

Special case analyses of the main results

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.