Janusz SOKOL, Ravinder Krishna RAINA, Nihal ÖZGÜR YILMAZ

Applications of k-Fibonacci numbers for the starlike analytic functions

Yayın Aralığı: 6
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

The k-Fibonacci numbers Fk,n (k > 0), deﬁned recursively by Fk,0 = 0,Fk,1 = 1 and Fk,n = kFk,n + Fk,n−1 for n ≥ 1 are used to deﬁne a new class SLk. The purpose of this paper is to apply properties of k-Fibonacci numbers to consider the classical problem of estimation of the Fekete Szegö problem for the class SLk. An application for inverse functions is also given. 2000 AMS Classiﬁcation: Primary 30C45, secondary 30C80

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[1] M. Fekete, G. Szegö, Eine Bemerung über ungerade schlichte Functionen, J. Lond. Math. Soc. 8(1933) 8589.
[2] C. Pommerenke, Univalent Functions, in: Studia Mathematica Mathematische Lehrbucher, Vandenhoeck and Ruprecht, 1975.
[3] J. Sokół, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175(23)(1999), 111116.
[4] J. Sokół, Remarks on shell-like functions, Folia Scient. Univ. Tech. Resoviensis 181(24)(2000), 111115.
[5] N. Yilmaz Özgür, J. Sokół, On starlike functions connected with k-Fibonacci numbers, Bull. Malaysian Math. Sci. Soc. 38(1)(2015), 249-258.