A Comprehensive Family of Biunivalent Functions Defined by k-Fibonacci Numbers

Abstract

By using k-Fibonacci numbers, we present a comprehensive family of regular and biunivalent functions of the type gz=z+∑j=2∞ djzj in the open unit disc 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.