A Comprehensive Family of Biunivalent Functions Defined by<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>k</a:mi></a:math>-Fibonacci Numbers

By using <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"><a:mi>k</a:mi></a:math> -Fibonacci numbers, we present a comprehensive family of regular and biunivalent functions of the type <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"><c:mi>g</c:mi><c:mfenced open="(" close=")"><c:mrow><c:mi>z</c:mi></c:mrow></c:mfenced><c:mo>=</c:mo><c:mi>z</c:mi><c:mo>+</c:mo><c:msubsup><c:mrow><c:mo>∑</c:mo></c:mrow><c:mrow><c:mi>j</c:mi><c:mo>=</c:mo><c:mn>2</c:mn></c:mrow><c:mrow><c:mo>∞</c:mo></c:mrow></c:msubsup><c:mtext> </c:mtext><c:msub><c:mrow><c:mi>d</c:mi></c:mrow><c:mrow><c:mi>j</c:mi></c:mrow></c:msub><c:msup><c:mrow><c:mi>z</c:mi></c:mrow><c:mrow><c:mi>j</c:mi></c:mrow></c:msup></c:math> in the open unit disc <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"><g:mi mathvariant="fraktur">D</g:mi></g:math> . 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.