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

Abstract

In this work, we consider certain class of bi-univalent functions related with shell-like curves related to κ−Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third coefficients) and Fekete -Szegö inequalities. Also we discuss the special cases of the obtained results.

New Subclasses of Bi-Univalent Functions based on the Fibonacci Numbers

“…Other few papers that also introduced and investigated new subclasses with Sakaguchi functions related to Fibonacci numbers are [18], [24] and [35]. Defining new subclasses of analytic biunivalent functions and investigating certain geometric properties associated with the Fibonacci numbers are also among the studies that have received much attention from researchers (see [2], [25], [30], [14], [31], [20], [15]).…”