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1
Content available remote k-Fold symmetrical mappings and loewner chains
EN
Let B be the unit ball in Cn with respect to an arbitrary norm on Cn. In this paper, we give a necessary and su.cient condition that a Loewner chain f(z, t), such that {e-tf(z, t)}t is more than or equal to 0 is a normal family on B, is k-fold symmetrical. As a corollary, we give a necessary and su.cient condition that a normalized locally biholomorphic mapping on B is spirallike of type and k-fold symmetrical. When alpha = 0, this result solves a natural problem that is similar to an open problem posed by Liczberski. We also give two examples of k-fold symmetrical Loewner chains.
2
Content available remote A class of rational mappings in several complex variables
EN
In this paper, we will give coefficient conditions for mappings of the form f(z) = z/(1+sum for k=1 bkzk1 to infinity) to be starlike or convex on the Euclidean unit ball B in Cn. Our results give concrete examples of strongly starlike mappings of order a, starlike mappings of order a and convex mappings on B.
EN
Let B be the unit ball of Cn with respect to the Euclidean norm and f[z,t} be a Loewner chain. In this paper we study certain properties of f(z,t) and we obtain a sufficient condition for the transition mapping associated to f(z,t) to generate this chain.
4
Content available remote On some sufficient conditions for univalence in complex Banach spaces
EN
In this paper, we will consider some sufficient conditions for locally biholomorphic mappings defined in the unit ball in complex Banach spaces to be biholomorphic and to have (phi)-like images. As a corollary, we obtain some sufficient condition for locally biholomorphic mappings to be starlike mappings.
EN
In this paper, we will consider classes of subordinations involving partial derivatives of holomorphic mappings in complex Banach spaces.
EN
In this paper we will give some conditions of spirallikeness for holomorphic mappings defined on bounded balanced pseudoconvex domains in Cn with C1 plurisubharmonic defining functions.
7
Content available remote On some alpha convex mappings on the unit ball Cn
EN
In this paper the author defined the notion of alpha-convexity of order gamma in the se
8
Content available remote Certain sufficient conditions of injectivity in Cn
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