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On Sakaguchi functions.

Yang, Ding-Gong, Liu, Jin-Lin (2003)

International Journal of Mathematics and Mathematical Sciences

On semi-typically real functions

Leopold Koczan, Katarzyna Trąbka-Więcław (2009)

Annales UMCS, Mathematica

Suppose that A is the family of all functions that are analytic in the unit disk Δ and normalized by the condition [...] For a given A ⊂ A let us consider the following classes (subclasses of A): [...] and [...] where [...] and S consists of all univalent members of A.In this paper we investigate the case A = τ, where τ denotes the class of all semi-typically real functions, i.e. [...] We study relations between these classes. Furthermore, we find for them sets of variability of initial coeffcients,...

On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane

Ewa Ligocka (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every f and w ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and l i m R e z - ( g ( w ) - w ) = 0 .

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