Schwarz Type Lemmas for Generalized Harmonic Functions

Let α , β ∈ ( - 1 , ∞ ) such that α + β > - 1 . Given two continuous functions g ∈ C ( D ¯ ) and f ∈ C ( T ) , we provide various Schwarz type lemmas for mappings u satisfying the inhomogeneous ( α , β ) -harmonic equation L α , β u = g in D and u = f in T , where D is the unit disc of the comple...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 47; no. 2
Main Authors Khalfallah, Adel, Mhamdi, Mohamed
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.03.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Continuity (mathematics)
Harmonic functions
Mathematics
Mathematics and Statistics
Weighted Green function
Schwarz lemma
Harmonic mapping
Primary: 31A30
Schwarz–Pick lemma
35J25
Harmonic equation
Secondary: 31A05
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Summary:Let α , β ∈ ( - 1 , ∞ ) such that α + β > - 1 . Given two continuous functions g ∈ C ( D ¯ ) and f ∈ C ( T ) , we provide various Schwarz type lemmas for mappings u satisfying the inhomogeneous ( α , β ) -harmonic equation L α , β u = g in D and u = f in T , where D is the unit disc of the complex plane C and T = ∂ D is the unit circle. The obtained results provide a significant improvement over previous research on the subject.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01646-4