Analytic and geometric properties associated with some extension operators

Chirilă, Teodora

doi:10.1080/17476933.2012.746966

Cited by 9 publications

(3 citation statements)

References 26 publications

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“…Corollary 2.1 was obtained in [18], in the case γ = 0. Also, Corollary 2.1 was recently obtained in [6], in the case α = 0.…”

Section: The Operator φ Nαβ and G-loewner Chainsmentioning

confidence: 73%

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An Extension Operator Associated With Certain $G$-Loewner Chains

Chirilă¹

2013

Taiwanese J. Math.

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In this paper we are concerned with an extension operator Φ n,α,β that provides a way of extending a locally univalent function f on the unit disc U to a locally biholomorphic mapping F ∈ H(B n ). By using the method of Loewner chains, we prove that if f can be embedded as the first element of a g-Loewner chain on the unit disc, whereAlso, if f is spirallike of type δ and order γ on U , where δ ∈ (−π/2, π/2) and γ ∈ (0, 1), then F = Φ n,α,β (f) is spirallike of type δ and order γ on B n . We also obtain a subordination preserving result under the operator Φ n,α,β and we consider some radius problems associated with this operator.

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“…Corollary 2.1 was obtained in [18], in the case γ = 0. Also, Corollary 2.1 was recently obtained in [6], in the case α = 0.…”

Section: The Operator φ Nαβ and G-loewner Chainsmentioning

confidence: 73%

“…This result was obtained in [18], in the case γ = 0. In the case α = 0 and γ ∈ (0, 1), Theorem 2.1 was recently obtained in [6].…”

Section: The Operator φ Nαβ and G-loewner Chainsmentioning

confidence: 94%

An Extension Operator Associated With Certain $G$-Loewner Chains

Chirilă¹

2013

Taiwanese J. Math.

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“…For Q ≡ 0, the extension operator Φ n,Q reduces to the extension operator Φ n . The extension operator Φ n,Q preserves parametric representation and starlikeness if Q ≤ 1/4 (see [10]), convexity if Q ≤ 1/2 ( see [16]) and starlikeness of order α ∈ (0, 1) if Q ≤ 1−|2α−1| 8α (see [21]; see also [2]). In a recent study, there has been investigated results concerning extended Loewner chains and this extension operator, as well as other preservation results (see [15]).…”

Section: Preliminariesmentioning

confidence: 99%

Extension operators and Janowski starlikeness with complex coe cients

Manu

2023

Stud. Univ. Babes-Bolyai Math.

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"In this paper, we obtain certain generalizations of some results from [13] and [14]. Let $\Phi_{n, \alpha, \beta}$ be the extension operator introduced in \cite{GrahamHamadaKohrSuffridge} and let $\Phi_{n, Q}$ be the extension operator introduced in [7]. Let $a \in \C$, $b \in \R$ be such that $|1-a| < b \leq {\rm Re}\ a$. We consider the Janowski classes $S^*(a,b, \B)$ and $\A S^*(a,b, \B)$ with complex coefficients introduced in [16]. In the case $n=1$, we denote $S^*(a,b, \mathbb{B}^1)$ by $S^*(a,b)$ and $\A S^*(a,b, \mathbb{B}^1)$ by $\A S^*(a,b)$. We shall prove that the following preservation properties concerning the extension operator $\Phi_{n, \alpha, \beta}$ hold: $\Phi_{n, \alpha, \beta} (S^*(a,b)) \subseteq S^*(a,b, \B)$, $\Phi_{n, \alpha, \beta} (\A S^*(a,b)) \subseteq \A S^*(a,b, \B)$. Also, we prove similar results for the extension operator $\Phi_{n, Q}$: $$\Phi_{n, Q}(S^*(a,b)) \subseteq S^*(a,b, \B),\ \Phi_{n, Q}(\A S^*(a,b)) \subseteq \A S^*(a,b, \B).$$ "

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Extension Operators that Preserve Geometric and Analytic Properties of Biholomorphic Mappings

Chirilă

2014

Topics in Mathematical Analysis and Applications

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Analytic and geometric properties associated with some extension operators

Cited by 9 publications

References 26 publications

An Extension Operator Associated With Certain $G$-Loewner Chains

An Extension Operator Associated With Certain $G$-Loewner Chains

Extension operators and Janowski starlikeness with complex coe cients

Extension Operators that Preserve Geometric and Analytic Properties of Biholomorphic Mappings

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