Construction of subclasses of univalent harmonic mappings
Sumit Nagpal, V. Ravichandran
TL;DR
This paper introduces a new method to construct subclasses of univalent harmonic mappings from analytic functions, defines a harmonic Alexander integral operator, and determines the convexity radius for specific harmonic function families.
Contribution
It presents a novel methodology for constructing subclasses of univalent harmonic mappings and introduces the harmonic Alexander integral operator.
Findings
Constructed subclasses of univalent harmonic mappings.
Defined the harmonic Alexander integral operator.
Determined the radius of convexity for certain harmonic function families.
Abstract
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notion of harmonic Alexander integral operator is introduced. Also, the radius of convexity for certain families of harmonic functions is determined.
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Taxonomy
TopicsAnalytic and geometric function theory · Differential Equations and Boundary Problems