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Certain subclasses of analytic functions with complex order.

A Selvam1, P Sooriya Kala, N Marikkannan

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Summary
This summary is machine-generated.

Two new subclasses of analytic functions of complex order were introduced. Coefficient bounds and inclusion relationships for their (n-δ) neighborhoods were established.

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Area of Science:

  • Complex analysis
  • Geometric function theory

Background:

  • Analytic functions are fundamental in complex analysis.
  • Neighborhoods of analytic functions provide insights into their geometric properties.

Purpose of the Study:

  • Introduce two novel subclasses of analytic functions of complex order.
  • Investigate coefficient bounds for these new subclasses.
  • Examine inclusion relationships involving (n-δ) neighborhoods for these functions.

Main Methods:

  • Definition of new function subclasses.
  • Application of analytic function theory principles.
  • Utilizing neighborhood concepts in complex analysis.

Main Results:

  • Established coefficient bounds for the newly defined subclasses.
  • Demonstrated inclusion relationships for (n-δ) neighborhoods of these analytic functions.
  • Analysis focused on functions with negative coefficients.

Conclusions:

  • The study expands the understanding of analytic functions of complex order.
  • The findings contribute to the geometric function theory by characterizing new subclasses and their neighborhoods.