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By using  k -Fibonacci numbers, we present a comprehensive family of regular and biunivalent functions of the type  g z = z + ∑ j = 2 ∞   d j z j 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.

A Comprehensive Family of Biunivalent Functions Defined byk-Fibonacci Numbers

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