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Differential Subordination of Certain Class of Starlike Functions

Neha Verma, S. Sivaprasad Kumar

Abstract

This paper presents several results concerning second and third-order differential subordination for the class $\mathcal{S}^{*}_{e}:=\{f\in \mathcal{A}:zf'(z)/f(z)\prec e^z\}$, which represents the class of starlike functions associated with exponential function.

Differential Subordination of Certain Class of Starlike Functions

Abstract

This paper presents several results concerning second and third-order differential subordination for the class , which represents the class of starlike functions associated with exponential function.
Paper Structure (3 sections, 28 theorems, 89 equations, 1 figure, 1 table)

This paper contains 3 sections, 28 theorems, 89 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results

Key Result

Lemma A

antoninoandmiller Let $z_0\in \mathbb{D}$ and $r_0=|z_0|$. Let $f(z)=a_nz^n+a_{n+1}z^{n+1}+\cdots$ be continuous on $\overline{\mathbb{D}}_{r_0}$ and analytic on $\mathbb{D}\cup\{z_0\}$ with $f(z)\neq 0$ and $n\geq 2$. If $|f(z_0)|=\max \{|f(z)|:z\in \overline{\mathbb{D}}_{r_0}\}$ and $|f'(z_0)|=\ma

Figures (1)

  • Figure 1: Graph of two circles, namely $C_1$ (blue boundary) and $C_2$ (orange boundary). While the shaded region (solid purple) represents $z+\sqrt{1+z^2}$.

Theorems & Definitions (46)

  • Definition 1.1
  • Lemma A
  • Definition 2.1
  • Lemma B
  • Lemma C
  • Lemma D
  • Lemma E
  • Lemma F
  • Theorem 3.1
  • proof
  • ...and 36 more