In this article, we establish the Bohr inequalities for the sense-preserving K-quasiconformal harmonic mappings defined in the unit disk <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb {D}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">D</mi> </math></EquationSource> </InlineEquation> associated with the subclasses of Ma-Minda starlike and convex univalent functions denoted by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {S}^*(\psi )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="script">S</mi> </mrow> <mo>∗</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {C}(\psi )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">C</mi> <mo stretchy="false">(</mo> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> respectively, and for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\log (f(z)/z)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>log</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">/</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> where f belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate the Logarithmic coefficient’s bounds for the functions in the subclass <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathcal {C}(\psi )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">C</mi> <mo stretchy="false">(</mo> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> when <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\psi (\mathbb {D})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">D</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is convex, which complement the result for starlike functions.

Bohr phenomenon for K-Quasiconformal harmonic mappings and logarithmic power series

期刊论文
发表日期：

2026年3月1日

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Kamaljeet Gangania,
Shivani Sharma

摘要

In this article, we establish the Bohr inequalities for the sense-preserving K-quasiconformal harmonic mappings defined in the unit disk $\mathbb {D}$ $D$ associated with the subclasses of Ma-Minda starlike and convex univalent functions denoted by $\mathcal {S}^*(\psi )$ $S^{*} (ψ)$ and $\mathcal {C}(\psi )$ $C (ψ)$ respectively, and for $\log (f(z)/z)$ $log (f (z) / z)$ where f belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate the Logarithmic coefficient’s bounds for the functions in the subclass $\mathcal {C}(\psi )$ $C (ψ)$ when $\psi (\mathbb {D})$ $ψ (D)$ is convex, which complement the result for starlike functions.