Abstract
In this paper, we introduce and investigate new subclasses of bi-univalent functions related to k-Fibonacci numbers. Furthermore, we nd estimates of first two coecients of functions in these classes. Also, we obtain the Fekete-Szego inequalities for these function classes.
Highlights
Let D = fz : jzj < 1g be the unit disc in the complex plane
We introduce and investigate new subclasses of biunivalent functions related to k-Fibonacci numbers
Since f 2 has the Maclaurin series given by (1), a computation shows that its inverse g = f 1 has the expansion g(w) = f 1(w) = w a2w2 + (2a22 a3)w3 + : (2)
Summary
In the following theorem we determine the initial Taylor coe¢ cients ja2j and ja3j for the function class SLMk; (pek(z)). If we can take the parameter = 0 and = 1 in the above theorem, we have the following the initial Taylor coe¢ cients ja2j and ja3j for the function classes SLk (p~k(z)) and KSLk (p~k(z)); respectively. If we can take the parameter k = 1 in the above corollaries, we have the following the initial Taylor coe¢ cients ja2j and ja3j for the function classes SL (p~(z)) and KSL (p~(z)); respectively, which were obtained in [6] by Güney et al. Corollary 12. By taking = 1 and = 0 in the above theorem, we have the initial Taylor coe¢ cients ja2j and ja3j for the function classes SLk (p~k(z)) and KSLk (p~k(z)); as stated in Corollary and Corollary respectively.
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