Schwarzian derivative for convex mappings of order α

Pablo Carrasco; Rodrigo Hernández

doi:10.1007/s13324-023-00785-y

Schwarzian derivative for convex mappings of order α

Pablo Carrasco
, Rodrigo Hernández

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The main purpose of this paper is to obtain sharp bounds of the norm of Schwarzian derivative for convex mappings of order alpha in terms of the value of f^{′ ′}(0 ) , in particular, when this quantity is equal to zero. In addition, we obtain sharp bounds for distortion and growth for this mappings and we generalize the results obtained by Suita (J Hokkaido Univ Ed Sect II A 46(2):113–117, 1996) and Yamashita (Hokkaido Math J 28:217–230, 1999) for this particular case.

Original language	English
Article number	22
Journal	Analysis and Mathematical Physics
Volume	13
Issue number	2
DOIs	https://doi.org/10.1007/s13324-023-00785-y
State	Published - Apr 2023
Externally published	Yes

Keywords

Convex of order alpha
Schwarz Lemma
Schwarzian derivative

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10.1007/s13324-023-00785-y

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title = "Schwarzian derivative for convex mappings of order α",

abstract = "The main purpose of this paper is to obtain sharp bounds of the norm of Schwarzian derivative for convex mappings of order alpha in terms of the value of f′ ′(0 ) , in particular, when this quantity is equal to zero. In addition, we obtain sharp bounds for distortion and growth for this mappings and we generalize the results obtained by Suita (J Hokkaido Univ Ed Sect II A 46(2):113{\textendash}117, 1996) and Yamashita (Hokkaido Math J 28:217{\textendash}230, 1999) for this particular case.",

keywords = "Convex of order alpha, Schwarz Lemma, Schwarzian derivative",

author = "Pablo Carrasco and Rodrigo Hern{\'a}ndez",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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doi = "10.1007/s13324-023-00785-y",

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AU - Carrasco, Pablo

AU - Hernández, Rodrigo

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AB - The main purpose of this paper is to obtain sharp bounds of the norm of Schwarzian derivative for convex mappings of order alpha in terms of the value of f′ ′(0 ) , in particular, when this quantity is equal to zero. In addition, we obtain sharp bounds for distortion and growth for this mappings and we generalize the results obtained by Suita (J Hokkaido Univ Ed Sect II A 46(2):113–117, 1996) and Yamashita (Hokkaido Math J 28:217–230, 1999) for this particular case.

KW - Convex of order alpha

KW - Schwarz Lemma

KW - Schwarzian derivative

UR - https://www.scopus.com/pages/publications/85147533426

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DO - 10.1007/s13324-023-00785-y

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VL - 13

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

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ER -

Schwarzian derivative for convex mappings of order α

Abstract

Keywords

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