A Characterization of Concave Mappings Using the Carathéodory Class and Schwarzian Derivative

Víctor Bravo; Rodrigo Hernández; Osvaldo Venegas

doi:10.1007/s40315-024-00557-0

A Characterization of Concave Mappings Using the Carathéodory Class and Schwarzian Derivative

Víctor Bravo, Rodrigo Hernández, Osvaldo Venegas

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

Abstract

The purpose of this paper is to establish new characterizations of concave functions f defined in D in terms of the operator 1+zf^′′/f^′, the Schwarzian derivative and the lower order. We will distinguish the cases when the omitted set is bounded or unbounded, and in the latter case, we will address the subclasses determined by the angle at infinity.

Original language	English
Journal	Computational Methods and Function Theory
DOIs	https://doi.org/10.1007/s40315-024-00557-0
State	Accepted/In press - 2024
Externally published	Yes

Keywords

30C45
30C55
31A10
CarathÃ©odory class
Concave mappings
Primary
Schwarzian derivative
Secondary

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10.1007/s40315-024-00557-0

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abstract = "The purpose of this paper is to establish new characterizations of concave functions f defined in D in terms of the operator 1+zf′′/f′, the Schwarzian derivative and the lower order. We will distinguish the cases when the omitted set is bounded or unbounded, and in the latter case, we will address the subclasses determined by the angle at infinity.",

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author = "V{\'i}ctor Bravo and Rodrigo Hern{\'a}ndez and Osvaldo Venegas",

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doi = "10.1007/s40315-024-00557-0",

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AU - Bravo, Víctor

AU - Hernández, Rodrigo

AU - Venegas, Osvaldo

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2024

Y1 - 2024

N2 - The purpose of this paper is to establish new characterizations of concave functions f defined in D in terms of the operator 1+zf′′/f′, the Schwarzian derivative and the lower order. We will distinguish the cases when the omitted set is bounded or unbounded, and in the latter case, we will address the subclasses determined by the angle at infinity.

AB - The purpose of this paper is to establish new characterizations of concave functions f defined in D in terms of the operator 1+zf′′/f′, the Schwarzian derivative and the lower order. We will distinguish the cases when the omitted set is bounded or unbounded, and in the latter case, we will address the subclasses determined by the angle at infinity.

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KW - 30C55

KW - 31A10

KW - Concave mappings

KW - Primary

KW - Schwarzian derivative

KW - Secondary

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JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

ER -

A Characterization of Concave Mappings Using the Carathéodory Class and Schwarzian Derivative

Abstract

Keywords

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