Region of variability for certain classes of univalent functions satisfying differential inequalities
S. Ponnusamy (IIT Madras, India), A. Vasudevarao (IIT Madras, India), and M. Vuorinen (University of Turku, Finland)
TL;DR
This paper determines the region of variability for specific subclasses of univalent functions that satisfy differential inequalities, providing graphical illustrations for various parameter sets.
Contribution
It introduces a method to explicitly find the variability region for subclasses of univalent functions constrained by differential inequalities.
Findings
Explicit regions of variability for certain univalent function subclasses
Graphical representations of these regions for different parameters
Enhanced understanding of the geometric behavior of these functions
Abstract
In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of parameters.
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Taxonomy
TopicsAnalytic and geometric function theory · Differential Equations and Boundary Problems · Holomorphic and Operator Theory