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Fixed points of difference operator of meromorphic functions
1School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China.
Thescientificworldjournal
|February 25, 2014
Summary
This study proves transcendental meromorphic functions of order less than one have infinitely many fixed points for their exact difference. This extends previous research on fixed points for such functions.
Area of Science:
- Complex Analysis
- Nevanlinna Theory
Background:
- Transcendental meromorphic functions are central to complex analysis.
- Understanding fixed points of function differences is crucial for analyzing function dynamics.
Purpose of the Study:
- To investigate the existence of fixed points for the exact difference Δf = f(z+1) - f(z).
- To extend existing theorems regarding fixed points of meromorphic functions.
Main Methods:
- Utilizing concepts from Nevanlinna theory, specifically Borel exceptional values (or Nevanlinna deficiency values).
- Analyzing the properties of transcendental meromorphic functions with order less than one.
Main Results:
- Proving that the exact difference Δf has infinitely many fixed points.
- Establishing this result when specific values (a ∈ ℂ and ∞) are Borel exceptional values of f.
Conclusions:
- The findings confirm and extend prior results by Chen and Shon.
- This research contributes to the understanding of fixed point theory in complex analysis.
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