Some Properties of Mappings Admitting General Poisson Representations

Adel Khalfallah; Miodrag Mateljević; Mohamed Mhamdi

doi:10.1007/s00009-021-01827-0

Some Properties of Mappings Admitting General Poisson Representations

Adel Khalfallah^*
, Miodrag Mateljević
, Mohamed Mhamdi

^*Corresponding author for this work

Department of Mathematics

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

18 Scopus citations

Abstract

The aim of this paper is twofold. First, we adapt the Burgeth’s spherical cap method [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burgeth] to the planar case to establish some Schwarz type lemmas for mappings admitting general Poisson type representations on the unit disk. Second, we prove a Landau type theorem for T_α-harmonic functions introduced by Olofsson (J Anal Math 123:227–249, 2014).

Original language	English
Article number	193
Journal	Mediterranean Journal of Mathematics
Volume	18
Issue number	5
DOIs	https://doi.org/10.1007/s00009-021-01827-0
State	Published - Oct 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Landau Theorem
Schwarz’s Lemma
T-harmonic mappings

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-021-01827-0

Cite this

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title = "Some Properties of Mappings Admitting General Poisson Representations",

abstract = "The aim of this paper is twofold. First, we adapt the Burgeth{\textquoteright}s spherical cap method [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burgeth] to the planar case to establish some Schwarz type lemmas for mappings admitting general Poisson type representations on the unit disk. Second, we prove a Landau type theorem for Tα-harmonic functions introduced by Olofsson (J Anal Math 123:227–249, 2014).",

keywords = "Landau Theorem, Schwarz{\textquoteright}s Lemma, T-harmonic mappings",

author = "Adel Khalfallah and Miodrag Mateljevi{\'c} and Mohamed Mhamdi",

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doi = "10.1007/s00009-021-01827-0",

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T1 - Some Properties of Mappings Admitting General Poisson Representations

AU - Khalfallah, Adel

AU - Mateljević, Miodrag

AU - Mhamdi, Mohamed

PY - 2021/10

Y1 - 2021/10

N2 - The aim of this paper is twofold. First, we adapt the Burgeth’s spherical cap method [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burgeth] to the planar case to establish some Schwarz type lemmas for mappings admitting general Poisson type representations on the unit disk. Second, we prove a Landau type theorem for Tα-harmonic functions introduced by Olofsson (J Anal Math 123:227–249, 2014).

AB - The aim of this paper is twofold. First, we adapt the Burgeth’s spherical cap method [Manuscripta Math. 77:283–291, 1992 by Burgeth and Proceedings of the NATO Advanced Research Workshop on Classical and Modem Potential Theory and Applications, pp 133–147, 1994 by Burgeth] to the planar case to establish some Schwarz type lemmas for mappings admitting general Poisson type representations on the unit disk. Second, we prove a Landau type theorem for Tα-harmonic functions introduced by Olofsson (J Anal Math 123:227–249, 2014).

KW - Landau Theorem

KW - Schwarz’s Lemma

KW - T-harmonic mappings

UR - https://www.scopus.com/pages/publications/85112739811

U2 - 10.1007/s00009-021-01827-0

DO - 10.1007/s00009-021-01827-0

M3 - Article

AN - SCOPUS:85112739811

SN - 1660-5446

VL - 18

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 5

M1 - 193

ER -

Some Properties of Mappings Admitting General Poisson Representations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this