Normality of Composite Analytic Functions and Sharing an Analytic Function
Copyright policy )Normality of Composite Analytic Functions and Sharing an Analytic Function
AbstractA result of Hinchliffe (2003) is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let "Equation missing" be an analytic function, "Equation missing" a family of analytic functions in a domain "Equation missing", and "Equation missing" a transcendental entire function. If "Equation missing" and "Equation missing" share "Equation missing" IM for each pair "Equation missing", and one of the following conditions holds: (1) "Equation missing" has at least two distinct zeros for any "Equation missing"; (2) "Equation missing" is nonconstant, and there exists "Equation missing" such that "Equation missing" has only one distinct zero "Equation missing", and suppose that the multiplicities "Equation missing" and "Equation missing" of zeros of "Equation missing" and "Equation missing" at "Equation missing", respectively, satisfy "Equation missing", for each "Equation missing", where "Equation missing"; (3) there exists a "Equation missing" such that "Equation missing" has no zero, and "Equation missing" is nonconstant, then "Equation missing" is normal in "Equation missing".
- Xinyang Normal University China (People's Republic of)
- Xinyang Normal University China (People's Republic of)
- Shaoguan University China (People's Republic of)
- Guangzhou University China (People's Republic of)
- Xinyang Normal University China (People's Republic of)
T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, Applied Mathematics, Geometry and Topology, Analysis
T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, Applied Mathematics, Geometry and Topology, Analysis
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