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<p>Under given coefficient conditions for analytic functions <Emphasis Type="BoldItalic">f</Emphasis> in the unit disk <b>D</b>, we first obtain the starlike and convex radii for the linear combination of the differential operator <i>zf</i> ′ of analytic functions <Emphasis Type="BoldItalic">f</Emphasis> in <b>D.</b> Then we obtain the starlike and convex radii for the differential operator <i>zf</i>′<i>.</i> Furthermore, we present the starlike and convex radii for the linear combination of the differential operator <i>zf</i>′ and analytic functions <Emphasis Type="BoldItalic">f</Emphasis> in <b>D.</b> Our results imply the related result obtained by Gavrilov [<i>Mat. Zametki</i>, <b>7</b>, 295–298 (1970)].</p>

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Sharp Starlike and Convex Radii for the Differential Operator of Analytic Functions

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Zhenyong Hu,
  • H. M. Srivastava,
  • Ying Zhang

摘要

Under given coefficient conditions for analytic functions f in the unit disk D, we first obtain the starlike and convex radii for the linear combination of the differential operator zf ′ of analytic functions f in D. Then we obtain the starlike and convex radii for the differential operator zf′. Furthermore, we present the starlike and convex radii for the linear combination of the differential operator zf′ and analytic functions f in D. Our results imply the related result obtained by Gavrilov [Mat. Zametki, 7, 295–298 (1970)].