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Coefficients and integral mean estimates for harmonic mappings via quasi-subordination
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- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 21 July 2026, pp. 1-22
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In this article, we study normalized univalent harmonic mappings associated with quasi-subordination. For the class $\mathcal {S}_{H_q}^0(\mathcal {S})$
, we establish the harmonic analog of the Bieberbach conjecture together with the corresponding sharp growth estimate. Under suitable additional assumptions on the quasi-subordination data, we obtain integral mean estimates for this class. We also derive analogous results for several significant subclasses of $\mathcal {S}^{0}_{H}$
, including the class of mappings with m-fold symmetric analytic and co-analytic parts, as well as the class of mappings admitting minimal surface lifts. By leveraging the flexibility of quasi-subordination, these findings extend and unify several earlier results in the study of univalent harmonic mappings.
UNIVALENT HARMONIC MAPPINGS INTO TWO-SLIT DOMAINS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 88 / Issue 1 / February 2010
- Published online by Cambridge University Press:
- 22 January 2010, pp. 61-73
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