Piotr Liczberski’s research while affiliated with Lodz University of Technology and other places

... Using (3-1), and (3)(4), we obtain k ∈ K. Let s(x) = (D H (x)) −1 D F(x) x, and let ...

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On the coefficient inequalities for some classes of holomorphic mappings in complex Banach spaces

... Using (3-1), and (3)(4), we obtain k ∈ K. Let s(x) = (D H (x)) −1 D F(x) x, and let ...

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On the coefficient inequalities for some classes of holomorphic mappings in complex Banach spaces

... In the papers [4,5] we gave for a few Bavrin's families a sharp estimate for the pair of homogeneous polynomials Q f ,2 , Q f ,1 , i.e., the sharp estimate ...

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Fekete–Szegö problem for Bavrin’s functions and close-to-starlike mappings in $${\mathbb {C}}^{n}

... Notably, when γ = 2, we obtain the class of odd univalent functions. Liczberski and Polubinski, in [3], extended this notion by developing the theory of (λ, γ)-symmetrical functions, where λ = 0, 1, 2, . . . , γ − 1 and γ = 2, 3, . . . . ...

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Defining and Analyzing New Classes Associated with (λ,γ)-Symmetrical Functions and Quantum Calculus

... However, Cartan [6] stated that the Bieberbach conjecture does not hold in several complex variables. In fact, only a few complete results are known for the inequalities of homogeneous expansions for subclasses of biholomorphic mappings in n (see, e.g., Długosz and Liczberski [7], Hamada and Honda [8], Liu and Wu [9], Liu and Liu [10], Liu et al. [11], and Xu et al. [12]). Many works are concentrating on the bounds of second-and third-order terms of homogeneous expansions for starlike mappings and the sharp bounds of all homogeneous expansions for the special subclasses of starlike mappings with some restricted conditions (see, e.g., Hamada et al. [13], Liu and Liu [14], Tu and Xiong [15], Xiong [16], Xu et al. [17], and Xu et al. [18]). ...

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Some results of homogeneous expansions for a class of biholomorphic mappings defined on a Reinhardt domain in ℂ

... We say that such mappings are of onedimensional type. This subclass has been studied by many mathematicians (see, for example, [3,12,24] and references therein). In this connection, the following fact is helpful (for detailed calculation see [8]). ...

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Multidimensional analogs of the Fekete--Szeg\"{o} functional

... In the proof of next theorem, we will use the following result form the paper [10]: ...

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Some propositonerties of a Bavrin’s family of holomorphic functions in Cn

... Continuing the first section we give a very useful functional symmetry. In the papers [3,6,11] there are considered the consequences of a modification of the above starlikeness factorization (1), using a unique decomposition of mappings f : B n → C n with respect to the cyclic group of k-th. roots of unity, k ≥ 2. Below we present such partition for mappings f : X ⊃ → Y, where X, Y are normed complex vector spaces and is a k-symmetric nonempty subset of X (ε = for the generator ε = exp 2πi k of the above group) [14]. ...

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On an Application of Jack’s Lemma, Starlikeness and k-Fold Symmetry in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^{n}$$\end{document}

... In [26] the notion of α-accessible domain was defined. It was shown that such domains posses the cone condition with l(p) = −p. ...

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Criteria of univalence and fully \alpha--accessibility for p--harmonic and p--analytic functions

... z -h(z) for zeB.Ii we show that R e m a r k 3. In [7], the second and third authors gave sufficient conditions for locally biholomorphic mappings on the unit ball with respect to an arbitrary norm on C n to be $-like mappings. The condition (i) is the same, but the right hand side of the condition (ii) in [7] is 1. ...

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On some sufficient conditions for univalence in complex Banach spaces