Abstract
For real numbers α and β such that 0≤α＜1＜β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.
Highlights
Re f z z .We remark that, for given real numbers and f z2 z and f z .we define an analytic function p : by 2πi 1 p π i log e 1 z z (1)The above function p was introduced by Kuroki and Owa [1] and they proved p maps onto a convex domain w : Re w, conformally
We find some relationships involving functions in the class T
We estimate the bounds of coefficients and solve Fekete-Szegö problem for functions in this class
Summary
The above function p was introduced by Kuroki and Owa [1] and they proved p maps onto a convex domain w : Re w , conformally. Using this fact and the definition of subordination, we can obtain the following Lemma, directly. We solve several coefficient problems including Fekete-Szegö problems for functions in the class. We estimate the bounds of initial coefficients of inverse functions and bi-univalent functions. For the coefficient bounds of functions in special subclasses of S , the readers may be referred to the works [2,3,4]
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