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Majorization problems for two subclasses of analytic functions connected with the Liu-Owa integral operator and

Huo Tang1, Guantie Deng2

  • 11School of Mathematics and Statistics, Chifeng University, Chifeng, People's Republic of China.

Journal of Inequalities and Applications
|October 27, 2018
PubMed
Summary

This study explores majorization properties for uniformly starlike and spiral-like functions, utilizing the Liu-Owa integral operator. Key findings reveal specific characteristics of these function classes under the defined operator.

Keywords:
Analytic functionExponential functionLiu–Owa integral operatorMajorizationSubordination

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Area of Science:

  • Complex Analysis
  • Geometric Function Theory

Background:

  • Uniformly starlike functions and spiral-like functions are important classes in geometric function theory.
  • The Liu-Owa integral operator is a key tool for defining and analyzing these functions.

Purpose of the Study:

  • To investigate majorization properties for uniformly starlike and spiral-like functions.
  • To analyze these properties in relation to a specific exponential function and the Liu-Owa integral operator.

Main Methods:

  • Utilizing the definition of the Liu-Owa integral operator.
  • Applying the concept of majorization to the specified classes of functions.

Main Results:

  • Established majorization properties for uniformly starlike functions.
  • Determined majorization properties for spiral-like functions related to an exponential function.

Conclusions:

  • The study provides new insights into the majorization behavior of these function classes.
  • The findings contribute to the understanding of integral operators in geometric function theory.