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Öğe SECOND HANKEL DETERMINANT PROBLEM FOR SEVERAL CLASSES OF ANALYTIC FUNCTIONS RELATED TO SHELL-LIKE CURVES CONNECTED WITH FIBONACCI NUMBERS(2018) İlhan, Sedat; Güney, Hatun Özlem; Sokol, JanuszIn this paper, we investigate upper bounds for the second Hankel determinant in several classes of analytic functions in the open unit disc, related to shell-likecurves and connected with Fibonacci numbers.Öğe SECOND HANKEL DETERMINANT PROBLEM FOR SEVERAL CLASSES OF ANALYTIC FUNCTIONS RELATED TO SHELL-LIKE CURVES CONNECTED WITH FIBONACCI NUMBERS(Turkic World Mathematical Soc, 2018) Sokol, Janusz; Ilhan, Sedat; Guney, H. OzlemIn this paper, we investigate upper bounds for the second Hankel determinant in several classes of analytic functions in the open unit disc, related to shell-like curves and connected with Fibonacci numbers.Öğe An upper bound for third Hankel determinant of starlike functions connected with k-Fibonacci numbers(Springer International Publishing Ag, 2019) Guney, H. Ozlem; Ilhan, Sedat; Sokol, JanuszIn this paper, we investigate the third Hankel determinant problem in some classes of analytic functions in the open unit disc connected with k-Fibonacci numbers Fk,n(k>0). For this, first, we prove a conjecture, posed in Guney et al. (2017), for sharp upper bound of the second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions. Finally, we give an upper bound for the third Hankel determinant in this class. The results presented in the present paper have been shown to generalize and improve some recent work of Soko et al. (2017).
