Versions of Koebe 1/4 theorem for analytic and quasiregular harmonic functions and applications | Zendy

Miodrag Mateljević | Zendy

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Versions of Koebe 1/4 theorem for analytic and quasiregular harmonic functions and applications

Author(s) -

Miodrag Mateljević

Publication year - 2008

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim0898061m

Subject(s) - holomorphic function , harmonic function , harmonic , mathematics , pure mathematics , analytic function , mathematical analysis , physics , quantum mechanics

In this paper we mainly survey results obtained in (MM3). For example, we give an elementary proof of two versions of Koebe 1/ 4t heorem for analytic functions (see Theorem 1.2 and Theorem 1.4 below). We also show a version of the Koebe theorem for quasiregular harmonic functions. As an application, we show that holomorphic functions (more generally quasiregular harmonic functions) and their modulus have similar behavior in a certain sense. 1. Two versions of Koebe 1/4 theorem for analytic functions This paper can be considered as the review of some results presented in (MM3), but it also contains new results and proofs. We will use the following notation. If r> 0a nda is a complex number B(a; r )= {z ∈ C : |z − a|

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