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Просмотр по автору "Wirths K."

Просмотр по автору "Wirths K."

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  • A proof of the Livingston conjecture 
    Avkhadiev F.; Wirths K. (2007)
    Let D denote the open unit disc and f : D → be meromorphic and injective in D. We further assume that f has a simple pole at the point p ∈ (0, 1) and an expansion . In particular, we consider functions f that map D onto a ...
  • Analogues to Landau’s Inequality for Nonvanishing Bounded Functions and for Bloch Functions 
    Kayumov I.; Wirths K. (2019)
    © 2018, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. Starting with some famous inequalities for unimodular bounded functions proved by E. Landau and O. Szász, we derive similar inequalities ...
  • Asymptotically sharp bounds in the Hardy-Littlewood inequalities on mean values of analytic functions 
    Avkhadiev F.; Wirths K. (2001)
    Let f be analytic in the unit disc, and let it belong to the Hardy space H p, equipped with the usual norm ∥f∥ p. It is known from the work of Hardy and Littlewood that for q > p, the constants C (p,q) :=sup{∫ 1 0(1 - r) ...
  • Basic coefficient inequalities 
    Avkhadiev F.; Wirths K. (2009)
    There are many books that systematically present coefficient problems in geometric function theory. We refer the reader to the excellent monographs by Goluzin [70], Goodman [73], Hayman [78], Pommerenke [128], and Duren ...
  • Basic Schwarz-Pick type inequalities 
    Avkhadiev F.; Wirths K. (2009)
    Let Ω ⊂ ℂ̄ and Π ⊂ ℂ̄ be two domains equipped by the Poincaré metric. We are concerned with the set A(ω, Π) = {f: ω → Π of functions locally holomorphic or meromorphic in Ω and, in general, multivalued. Let λΩ (z), z ∈ Ω, ...
  • Coefficient Inequalities for Bloch Functions 
    Kayumov I.; Wirths K. (2019)
    © 2019, Pleiades Publishing, Ltd. In this article we derive new estimates for the moduli of the Taylor coefficients of Bloch functions. We use one of these estimates to prove an inequality of an area type for such functions.
  • Coefficients problems for Bloch functions 
    Kayumov I.; Wirths K. (2019)
    © 2019, Springer Nature Switzerland AG. In this article we give a survey on different methods to estimate the values of functionals in the coefficients of Bloch functions.
  • Concave schlicht functions with bounded opening angle at infinity 
    Avkhadiev F.; Wirths K. (2005)
    Let D denote the open unit disc. In this article we consider functions f(z) = z + ∑n=2 ∞ an(f)zn that map D conformally onto a domain whose complement with respect to C is convex and that satisfy the normalization f(1) = ...
  • Introduction 
    Avkhadiev F.; Wirths K. (2009)
    The aim of the present book is a unified representation of some recent results in geometric function theory together with a consideration of their historical sources. These results are concerned with functions f, holomorphic ...
  • Multiply connected domains 
    Avkhadiev F.; Wirths K. (2009)
    In the preceding chapters we considered punishing factors for simply connected domains, except the case C2(Ω, Π). Namely, in Section 4.6 it was proved that for all hyperbolic domains Ω ⊂ ℂ̄ and Π ⊂ ℂ̄. © 2009 Birkhäuser Verlag AG.
  • On the best constants for the Brezis-Marcus inequalities in balls 
    Avkhadiev F.; Wirths K. (2012)
    We study the best possible constants c(n) in the Brezis-Marcus inequalities for u∈H01(Bn) in balls Bn={x∈Rn:|x-x0|<ρ}. The quantity c(1) is known by our paper [F.G. Avkhadiev, K.-J. Wirths, Unified Poincaré and Hardy ...
  • On the coefficient multipliers theorem of Hardy and Littlewood 
    Avkhadiev F.; Wirths K. (2002)
    Let an(f) be the Taylor coefficients of a holomorphic function f which belongs to the Hardy space Hp, 0 < p < 1. We prove the estimate C(p) ≤ πep/[p(1 - p)] in the Hardy-Littlewood inequality We also give explicit estimates ...
  • On the coefficients of concave univalent functions 
    Avkhadiev F.; Pommerenke C.; Wirths K. (2004)
    Let D denote the open unit disc and f : D → ℂ̄ be meromorphic and injective in D. We assume that f is holomorphic at zero and has the expansion f(z) = z + ∞σ anzn Especially, we consider f that map D onto a domain whose ...
  • On the Coefficients of Quasiconformality for Convex Functions 
    Avkhadiev F.; Wirths K. (2010)
    Let f be holomorpic and univalent in the unit disc E and f(E) be convex. We consider the conformal radius R = R(D,z) = {pipe;} f′(ζ){pipe;}(1-ζ̄) of D = f(E) at the point z = f(ζ). In [3] and [4] the coefficient kf(r), r ...
  • On the growth of nonvanishing analytic functions 
    Avhadiev F.; Schulte N.; Wirths K. (2000)
    In this article by a new and simple method we derive new and old coefficient bounds and distortion theorems for functions G(z) analytic in the unit disk and satisfying sup(|G(z)|(1 - |z|2)a) ≦ 1 for some a ≧ 0. These results ...
  • On the sum of squares of the coefficients of Bloch functions 
    Kayumov I.; Wirths K. (2019)
    © 2019, Springer-Verlag GmbH Austria, part of Springer Nature. In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved.
  • Punishing factors and Chua's conjecture 
    Avkhadiev F.; Wirths K. (2007)
    Let Ω and ∏ be two simply connected domains in the complex plane ℂ which are not equal to the whole plane ℂ. We are concerned with the set A(Ω, ∏) of functions f : Ω → ∏ holomorphic on Ω and we prove estimates for |f(n)(z)|, ...
  • Punishing factors for finitely connected domains 
    Avkhadiev F.; Wirths K. (2006)
    Let Ω and Π be two finitely connected hyperbolic domains in the complex plane ℂ and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic ...
  • Punishing factors for special cases 
    Avkhadiev F.; Wirths K. (2009)
    After a colloquium talk of the second author on estimates of the form f(n)(z) /n! ≤ Cc (Ω, Π) (λΩ(z))n/ λΠ(f(z)), f ∈ A(Ω Π), z ∈ Ω for simply connected domains Ω and Π in ℂ, Ch. Pommerenke ([132]) proposed to look at (5.1) ...
  • Related results 
    Avkhadiev F.; Wirths K. (2009)
    First, we will give an outline of the ideas and results that led to the conjectures of Chua. To our knowledge, E. Landau was the first who considered the possibility to follow G. Pick's program as indicated in the introduction ...

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