Subclasses of convex functions on the unit disc of the complex plane

In this paper we introduce some subclasses of normalized univalent functions, more exactly subclasses of S ⋆ , which we will call convex functions of degree n . The main tool used is the idea behind Alexander’s duality theorem between S ⋆ and K . Also, we present a necessary and sufficient condition...

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Bibliographic Details
Published in:São Paulo Journal of Mathematical Sciences Vol. 18; no. 1; pp. 312 - 326
Main Author: Aron, Mihai
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2024
Springer Nature B.V
Subjects:
Complex variables
Convex analysis
Convexity
Duality theorem
Estimates
Inequality
Mathematics
Mathematics and Statistics
Original Article
Theorems
Starlike functions
Geometric properties
Convexity criteria
35C45
Convex functions
Growth results
35C50
ISSN:1982-6907, 2316-9028, 2306-9028
Online Access:Get full text
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Summary:In this paper we introduce some subclasses of normalized univalent functions, more exactly subclasses of S ⋆ , which we will call convex functions of degree n . The main tool used is the idea behind Alexander’s duality theorem between S ⋆ and K . Also, we present a necessary and sufficient condition for convexity of degree n in two complex variables.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-023-00376-6