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1
Content available remote Estimations of the second coefficient of a univalent, bounded, symmetric and non-vanishing function by means of Loewner's parametric method
100%
Śladkowska J.
Annales Polonici Mathematici
|
1998
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tom 68
|
nr 2
119-123
EN
Let $𝓑₀^{(R)}(b)$ denote the class of functions F(z) = b + A₁z + A₂z² + ...$ analytic and univalent in the unit disk U which satisfy the conditions: F(U) ⊂ U, 0 ∉ F(U), $Im F^{(n)}(0) = 0$. Using Loewner's parametric method we obtain lower and upper bounds of A₂ in $𝓑₀^{(R)}(b)$ and functions for which these bounds are realized. The class $𝓑₀^{(R)}(b)$, introduced in [6], is a subclass of the class $𝓑_u$ of bounded, non-vanishing univalent functions in the unit disk. This last class and closely related ones have been studied by various authors in [1]-[4]. We mention in particular the paper of D. V. Prokhorov and J. Szynal [5], where a sharp upper bound for the second coefficient in $𝓑_u$ is given.
2
Content available remote On the estimate of the fourth-order homogeneous coefficient functional for univalent functions
100%
Gromova L. , Vasil'ev A.
Annales Polonici Mathematici
|
1996
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tom 63
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nr 1
7-12
EN
The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class 𝕊 of all univalent holomorphic functions $f(z) = z + ∑^{∞}_{n=2} c_n z^n$ in the unit disk. For real values p and q in some regions of the (p,q)-plane the estimates of this functional are obtained by the area method for univalent functions. Some new regions are found where the Koebe function is extremal.
3
Content available remote Even coefficient estimates for bounded univalent functions
80%
Prokhorov D.
Annales Polonici Mathematici
|
1993
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tom 58
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nr 3
267-273
EN
Extremal coefficient properties of Pick functions are proved. Even coefficients of analytic univalent functions f with |f(z)| < M, |z| < 1, are bounded by the corresponding coefficients of the Pick functions for large M. This proves a conjecture of Jakubowski. Moreover, it is shown that the Pick functions are not extremal for a similar problem for odd coefficients.
4
Content available remote On starlikeness of certain integral transforms
80%
Ponnusamy S.
Annales Polonici Mathematici
|
1991-1992
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tom 56
|
nr 3
227-232
EN
Let A denote the class of normalized analytic functions in the unit disc U = {z: |z| < 1}. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by $F(z) = ∫_0^z (f(t)/t)dt$ and $G(z) = (2/z) ∫_0^z g(t)dt$ are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref'(z) > -δ and Re g'(z) > -ϱ respectively in U.
5
Content available remote On some radius results for normalized analytic functions
80%
Kim Y. , Kwon E.
Annales Polonici Mathematici
|
1998
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tom 68
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nr 1
51-60
EN
We investigate some radius results for various geometric properties concerning some subclasses of the class 𝓢 of univalent functions.
6
Content available remote On the univalent, bounded, non-vanishing and symmetric functions in the unit disk
80%
Śladkowska J.
Annales Polonici Mathematici
|
1996
|
tom 64
|
nr 3
291-299
EN
The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.
7
Content available remote On functions satisfying more than one equation of Schiffer type
80%
Macura J. , Śladkowska J.
Annales Polonici Mathematici
|
1993
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tom 58
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nr 3
237-252
EN
The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type ($D_n$-equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.
8
Content available remote Subclasses of typically-real functions defined by Ruscheweyh derivative
60%
Lecko A. , Lecko M. , Yaguchi T.
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2008
|
tom Vol. 41, nr 4
823-832
EN
For each lambda>- 1 let TR(lambda) be the class of all functions f analytic in D= {z is an element of C : \z\ < 1} of the form f (z) = [...] having real coefficients and satisfying the condition [...] where Llambda denote the Ruscheweyh derivative. Some basic properties of functions in are presented.
9
Content available remote On coefficients' estimates of concave univalent functions
60%
Zaprawa P.
|
2010
|
tom Vol. 32
109-116
EN
In the class Co(p), p ∈ (0,1) of univalent concave functions with a pole at p we find some estimates on the third coefficient as well as the residuum of a function, while its second coefficient is fixed.
10
Content available remote Certain sufficienty conditions on Fox-Wright function
51%
Chaurasia V. , Parihar H.
|
2008
|
tom Vol. 41, nr 4
813-822
EN
The main object of this paper is to find certain conditions for the function [...] to be a member of certain subclasses of analytic functions. Our results provides generalization of some recent results due to Swaminathan [19] and Chaurasia and Srivastava [20].
11
Content available remote Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues
51%
Krushkal S.
Open Mathematics
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2007
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tom 5
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nr 3
551-580
EN
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to $$\widehat{\mathbb{C}}$$ are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = {z: |z| > 1} can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely, in the norm on the space of Schwarzian derivatives. Applications of this result to Fredholm eigenvalues are given. We also solve the old Kühnau problem on an exact lower bound in the inverse inequality estimating k(f) by ϰ(f), and in the related Ahlfors inequality.
12
Content available remote Subordinations and superordinations using the Dziok-Srivastava linear operator
51%
Oros G. I. , Oros O.
|
2009
|
tom Vol. 31
99-106
EN
By using the properties of the Dziok-Srivastava linear operator we obtain differential subordinations and superordinations by using functions from class A. A sandwich-type result is also given. Theorem 1 from the paper gives sufficient conditions such that a function f ∈ A to be starlike, convex and α-convex.
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