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Bohr-type inequalities of analytic functions
Ming-Sheng Liu1, Yin-Miao Shang1, Jun-Feng Xu2
11School of Mathematical Sciences, South China Normal University, Guangzhou, China.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study explores Bohr-type radii for analytic functions and their associated alternating series within the unit disk. Most derived results are proven to be sharp, offering precise bounds for these functions.
Area of Science:
- Complex Analysis
- Geometric Function Theory
Background:
- Bohr's inequality provides a fundamental bound for analytic functions.
- Extending Bohr's inequality to various forms and related series is an active area of research.
Purpose of the Study:
- Investigate Bohr-type radii for diverse Bohr-type inequalities of analytic functions.
- Determine the Bohr-type radius for alternating series linked to analytic function Taylor series.
Main Methods:
- Utilizing techniques from geometric function theory.
- Applying methods for analyzing inequalities of analytic functions.
Main Results:
- Established Bohr-type radii for several forms of Bohr-type inequalities.
- Determined the Bohr-type radius for associated alternating series.
- Demonstrated the sharpness of most obtained results.
Conclusions:
- The findings provide sharp bounds for analytic functions and their associated alternating series.
- This research contributes to a deeper understanding of Bohr-type phenomena in complex analysis.
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