A comprehensive family of biunivalent functions defined by \(k\)-Fibonacci numbers (Q823597)

Summary: By using \(k\)-Fibonacci numbers, we present a comprehensive family of regular and biunivalent functions of the type \(g(z)=z+\sum_{j = 2}^\infty d_j z^j\) in the open unit disc \(\mathfrak{D}\). We estimate the upper bounds on initial coefficients and also the functional of Fekete-Szegö for functions in this family. We also discuss few interesting observations and provide relevant connections of the result investigated.