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Study analytical function subordination properties by applying a novel linear operator.

Maryam S Majel1,1, Mustafa I Hameed1,1

  • 1University of Anbar, Ramadi, Al Anbar Governorate, Iraq.

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Summary
This summary is machine-generated.

This study introduces a new linear operator for analytic univalent functions, utilizing differential subordination to explore function characteristics. The research investigates properties of subordination and superordination, contributing to geometric function theory.

Keywords:
Best DominantConvex FunctionDerivative OperatorDifferential SubordinationHadamard Product.Univalent Function

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Area of Science:

  • Complex Analysis
  • Geometric Function Theory

Background:

  • Analytic univalent functions represent a significant area within complex analysis, studied since 1907 for their intricate geometric properties.
  • Geometric function theory integrates principles from both geometry and analysis.

Purpose of the Study:

  • To introduce and analyze a new linear operator, denoted as M(σ,μ)^(n,ς)Υ(s), within the domain of analytic univalent functions.
  • To explore the properties of differential subordination and superordination using this novel operator.

Main Methods:

  • The study employs the differential subordination technique to derive characteristics of the new linear operator.
  • Analysis involves the Hadamard product and properties of the Komatu integral operator.

Main Results:

  • Several properties related to subordination and superordination were derived using the new operator and Hadamard product.
  • The study investigated various aspects of subordination and superordination for a specific class of univalent functions.

Conclusions:

  • A new linear operator, M(σ,μ)^(n,ς)Υ(s), connected to the Dziok-Srivastava operator and Komatu integral operator, has been established.
  • The differential subordination technique was applied to derive specific properties of this new operator.