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<p>In this article, we consider certain class of harmonic mappings defined in the unit disk <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {D}=\{z\in \mathbb {C}: |z|&lt;1\}.\)</EquationSource> </InlineEquation> Then we obtain pre-Schwarzian norm estimate of functions in the class. Next, we show that functions in the considered class are univalent and close-to-convex. Moreover, we discuss some growth and distortion theorems for associated analytic and co-analytic parts of harmonic mappings in the class. At last, we present coefficient estimate for the analytic part.</p>

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Pre-Schwarzian norm estimate and characterization of certain harmonic mappings

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Sushil Pandit

摘要

In this article, we consider certain class of harmonic mappings defined in the unit disk \(\mathbb {D}=\{z\in \mathbb {C}: |z|<1\}.\) Then we obtain pre-Schwarzian norm estimate of functions in the class. Next, we show that functions in the considered class are univalent and close-to-convex. Moreover, we discuss some growth and distortion theorems for associated analytic and co-analytic parts of harmonic mappings in the class. At last, we present coefficient estimate for the analytic part.