Growth and covering theorems associated with the Roper-Suffridge extension operator
نویسندگان
چکیده
منابع مشابه
On the generalized Roper-Suffridge extension operator in Banach spaces
The generalized Roper-Suffridge extension operator in Banach spaces is introduced. We prove that this operator preserves the starlikeness on some domains in Banach spaces and does not preserve convexity in some cases. Furthermore, the growth theorem and covering theorem of the corresponding mappings are given. Some results of Roper and Suffridge and Graham et al. in Cn are extended to Banach sp...
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and Applied Analysis 3 In contrast to the modified Roper-Suffridge extension operator in the unit ball, it is natural to ask if we can modify the Roper-Suffridge extension operator on the Reinhardt domains. In this paper, we will introduce the following modified operator: F z ⎛ ⎝f z1 f ′ z1 n ∑ j 2 ajz pj j , ( f ′ z1 2z2, . . . , ( f ′ z1 nzn ⎞ ⎠ ′ 1.5 on the Reinhardt domainΩn,p2,...,pn . Wew...
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Let$mathbb{C}^n$ be the space of $n$ complex variables. Let$Omega_{n,p_2,ldots,p_n}$ be a complete Reinhardt on$mathbb{C}^n$. The Minkowski functional on complete Reinhardt$Omega_{n,p_2,ldots,p_n}$ is denoted by $rho(z)$. The concept ofspirallike mapping of type $beta$ and order $alpha$ is defined.So, the concept of the strong and almost spirallike mappings o...
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Abstract. This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let X be a finite dimensional normed space; let μ be a Radon measure on X and let Ω ⊆ X be a μ-measurable set. For λ ≥ 1, a μ-measurable set Sλ(a) ⊆ X is a λ-Morse set with tag a ∈ Sλ(a) if there is r > 0 such that B(a, r) ⊆ Sλ(a) ⊆ B(a, λr)...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04963-1