| 关于亚纯函数不动点和微分方程亚纯解几个结果的推广 |
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| 引用本文： | 王安斌,詹小平.关于亚纯函数不动点和微分方程亚纯解几个结果的推广[J].湖南师范大学教育科学学报,1996(2). |
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| 作者姓名： | 王安斌 詹小平 |
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| 作者单位： | 岳阳师专数学系，湖南师大数学系 |
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| 摘 要： | 设ｆ为超越亚纯函数，Ｒ（ｚ）为有理函数，Ｆ．Ｇｒｏｓｓ和Ｃ．ＣＹａｎｇ在［１］中猜测：当Ｒ（ｚ）分子，分母最高次数≥３时，Ｒ（ｆ）有无穷个不动点，并指出附加上条件Ｎ（ｒ，ｆ）＝Ｓ（ｒ，ｆ）时结论是成立的．Ｃ．Ｃ，Ｙａｎｇ在［２］中附加条件Ｎ（ｒ，ｆ）＝Ｓ（ｒ，ｆ）后证明了这一结论的正确性，本文减弱了这一附加条件。本文还改进了Ｃ．Ｃ．Ｙａｎｇ的另些结果和Ｇ．Ｐ．Ｂａｒｋｅｒ，Ａ．Ｐ．Ｓｉｎｇｈ关于微分方程亚纯解的两个结果．
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| 关 键 词： | 亚纯函数 级 微分方程 |
EXTENSIONS OF SOME RESURTS FOR FIXED POINT OF MEROMORPHIC FUNCTION AND MEROMORPHIC SOLUTION OF DIFFERENTIAL EQUATION |
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| Wang Anbing,Zhan Xiaoping.EXTENSIONS OF SOME RESURTS FOR FIXED POINT OF MEROMORPHIC FUNCTION AND MEROMORPHIC SOLUTION OF DIFFERENTIAL EQUATION[J].Journal of Educational Science of Hunan Normal University,1996(2). |
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| Authors: | Wang Anbing Zhan Xiaoping |
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| Abstract: | Let f(z) be a transcendental meromorphic function, R (z) be a rational function, F. Gross and C. C. Yang made a Comjecture in 1] that if R(z) is any rational function of weigt greater than 2, then R (f) has an infinite number of fixed points, and they pointed out in 2] that if f satisfies N(r, f) = S (r, f) then R (f) must have an infinrte number of fixpoints.In this paper, it is proved that the condition N( r, f) = S ( r, f) may be replaced by the weakened condition and some results of G. P. Barker and A. P. Singh are extended. |
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| Keywords: | Cmeromorphic function order differential equation |
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