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Milloux inequality of E-valued meromorphic function.
1School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China.
Thescientificworldjournal
|March 8, 2014
Summary
This study establishes the Milloux inequality for E-valued meromorphic functions in infinite-dimensional Banach spaces. The findings extend results on Borel exceptional values for scalar-valued functions.
Area of Science:
- Complex Analysis
- Functional Analysis
- Meromorphic Functions
Background:
- The study of inequalities for meromorphic functions is a significant area in complex analysis.
- Extending these inequalities to infinite-dimensional spaces presents unique challenges and opportunities.
Purpose of the Study:
- To establish the Milloux inequality for E-valued meromorphic functions, where E is an infinite-dimensional complex Banach space with a Schauder basis.
- To investigate the Borel exceptional values of such functions and their derivatives.
Main Methods:
- Utilizing techniques from complex analysis and functional analysis.
- Applying the concept of Schauder basis in an infinite-dimensional Banach space.
- Extending existing inequality theorems to a more general setting.
Main Results:
- The successful establishment of the Milloux inequality for E-valued meromorphic functions.
- Demonstration of extensions of results concerning Borel exceptional values for scalar-valued functions.
Conclusions:
- The established Milloux inequality provides a powerful tool for analyzing E-valued meromorphic functions.
- The results generalize and extend previous findings, contributing to the theory of meromorphic functions in infinite-dimensional spaces.
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