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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 1

Hadamard product of holomorphic mappings associated with the conic shaped domain

Syed Zakar Hussain Bukhari(Department of Mathematics, Mirpur University of Science and Technology, Mirpur-10250(AJK), Pakistan)0000-0002-5243-4252
Aamir Shahzad0000-0001-5255-0176
Pages
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Publication Date
2023-03-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Using certain conditions for functions in the class $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2}),$ we also define another class $\delta-\mathcal{UM}^{\ast}(\ell,\eta_{1},\eta_{2})$ and study some subordination related result.

📌 3 Key Takeaways

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Objective & Hypothesis:We define certain subclasses $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2})$ and $\delta-\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ of holomorphic mappings involving some differential inequalities.
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Key Findings & Data:We study sufficient conditions for $f\in \delta-\mathcal{UM}(\ell,\eta_{1}% ,\eta_{2}).$ We also discuss the characterization for $f\in \delta -\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ along with the coefficient bounds and other problems.
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Conclusion & Impact:Using certain conditions for functions in the class $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2}),$ we also define another class $\delta-\mathcal{UM}^{\ast}(\ell,\eta_{1},\eta_{2})$ and study some subordination related result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Caratheodory functions · convolution · subordination

Abstract

We define certain subclasses $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2})$ and $\delta-\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ of holomorphic mappings involving some differential inequalities. These functions are actually generalizations of some basic families of starlike and convex mappings. We study sufficient conditions for $f\in \delta-\mathcal{UM}(\ell,\eta_{1}% ,\eta_{2}).$ We also discuss the characterization for $f\in \delta -\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ along with the coefficient bounds and other problems. Using certain conditions for functions in the class $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2}),$ we also define another class $\delta-\mathcal{UM}^{\ast}(\ell,\eta_{1},\eta_{2})$ and study some subordination related result.

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Cite This Article

Bukhari, S. Z. H., Shahzad, A. (2023). Hadamard product of holomorphic mappings associated with the conic shaped domain. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 1. https://doi.org/10.31801/cfsuasmas.1061950

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