Titlebook: Schwarz-Pick Type Inequalities; Farit G. Avkhadiev,Karl-Joachim Wirths Book 2009 Birkhäuser Basel 2009 Area.Factor.Lemma.Schwarz lemma.ana

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Basic coefficient inequalities, Goluzin [70], Goodman [73], Hayman [78], Pommerenke [128], and Duren [60]. In this chapter we only mention a few classical results on coefficients which are closely connected with the topic of this book. Also, we give several new facts with short proofs that have until now been presented only in or

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Punishing factors for special cases,look at (5.1) in the following way. The quotient (λΩ(.))./λп(.) reflects the influence of the positions of the points . and . in Ω and ∏ on the nth derivative .(.), whereas the quantities C.(Ω, п) are factors punishing bad behaviour of Ω or ү at the boundary. This motivates the title of the present

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Some open problems,ains are involved. From this point of view, it seems natural that the difficulties become nearly insuperable, if one allows the points . ∈ Ω or .) ∈ п, or both to vary, and asks for the maximum. Nevertheless, there exists one problem of this type that has attracted researchers for many years because

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Introduction,ional condition we impose on these functions is the condition that the range .(Ω) is contained in a given domain ∏ ⊂ .. This fact will be denoted by . ∈ .(Ω, п). We shall describe how one may get estimates for the derivatives |. (.)|, . ∈ ℕ, . ∈ . (Ω, ∏) dependent on the position of . in Ω and .(z.) in п.

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1660-8046 the several analytic methods, readers will find many interes.This book discusses in detail the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. It is the first systematic account of the main results in this area. Recent results in geometri

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