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On certain subclass of meromorphic spirallike functions involving the hypergeometric function
1School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan 455000, China.
Thescientificworldjournal
|June 28, 2014
Summary
We introduce a new subclass of meromorphic spirallike functions, denoted M(m)(1)(θ, λ, η). This study establishes integral representations, convolution properties, and coefficient estimates for this new class.
Area of Science:
- Complex Analysis
- Geometric Function Theory
Background:
- Meromorphic functions are essential in complex analysis.
- Spirallike functions exhibit unique geometric properties.
Purpose of the Study:
- Introduce and investigate a novel subclass of meromorphic spirallike functions: M(m)(1)(θ, λ, η).
- Extend existing theories in geometric function theory.
Main Methods:
- Utilizing techniques from complex analysis.
- Applying methods for integral representations.
- Investigating convolution properties.
- Deriving coefficient estimates.
Main Results:
- Established integral representations for the new function subclass.
- Proved key convolution properties.
- Obtained coefficient estimates for M(m)(1)(θ, λ, η) functions.
- Extended findings from prior research.
Conclusions:
- The study successfully defined and analyzed the M(m)(1)(θ, λ, η) subclass.
- The derived results offer significant extensions to the field of meromorphic spirallike functions.
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