共查询到20条相似文献，搜索用时 483 毫秒
1.
SUN Yao-qiang MA Chao-wei 《重庆大学学报(英文版)》2007,6(4):287-290
The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831]. 相似文献
2.
LAN Fu-xiang LI Jiang-tao 《重庆大学学报(英文版)》2007,6(4):291-293
We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 (1): 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m>2k 4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f m(z)f (k)(z)=a??f (k)(z)?≤B or f m(z)f (k)(z)=a??f (z)?≥B, then F is normal in D. 相似文献
3.
LAI Li-ping LI Chun-hong 《重庆大学学报(英文版)》2007,6(4):278-282
The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions f and g which are not polynominals of degree less than a positive integer k, if f nf (k) and g ng (k) share (1,2), where n is another positive integer not less than k 10, then f nf (k) identically equals g ng (k) or f nf (k)g ng (k) identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academi? Scientiarum Fennic? Mathematica, 1997, 22: 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13(1): 44-48. (In Chinese)]. 相似文献
4.
MA Chao-weia WANG Yong-jun 《重庆大学学报(英文版)》2007,6(4):299-301
A normal theorem concerning meromorphic functions sharing values was proved with the method of Zalcman- Pang.The theorem is as follows. If for each f in F, all zeros of f-a have multiplicity at least k (k≥2), f and its k-th derivative function share a, and if f=b whenever its k-th derivative equal b, then F is normal in D. This theorem improved the result of Chen and Fang [Chen HH, Fang ML, Shared values and normal families of meromorphic functions, Journal of Mathematical Analysis and Applications, 2001, 260: 124-132]. 相似文献
5.
文章研究了亚纯函数的唯一性,得到了关于亚纯函数f(z)和g(z)分担5个小函数的一个唯一性定理. 相似文献
6.
本文研究了高阶齐次线性微分方程f（k）＋Ak-1（z）e^pk-1（z）f^（k-1）＋Ak-2（z）^e^pk-2（z）f（k-2）＋…＋A0（z）e^pk（z）f=0和f（k）＋（Ak-1（z）e^pk-1（z）＋D（k-1）（z））f（k-1）＋…＋（A0（z）ep0（z）＋D0（z））f=0解的增长性问题,其中Pjk（z）=ajz^n＋bj,lz^n-1＋…bj,n,Aj（z）和Dj（z）是有限级整函数。针对Pj（z）中aj（j=0,1,…k-1）的幅角主值不全相等的情形。得到了σ2（f）=∞。 相似文献
7.
研究全纯函数与其微分多项式分担函数,得到了如下的正规定则：设F是区域D内的全纯函数族,k是一正整数,h1（z）,h2（z）在区域D内的解析,满足｜h1（z）｜2＋｜h2（z）｜2≠0。若f∈F,f的零点重级至少为k,且f（z）=0｜f（k）（z）｜≤M（常数M〉0）,（z）=αi（z）L（Z）=αi（z）,i=1,2,其中L（z）=f∞（z）＋α1（z）f（k-1）（z）＋…＋αk（z）f（z）为f的微分多项式,αi（z）（i=1,2,…,k,k≥1）在D内解析,那么F在D内正规。 相似文献
8.
主要研究了具有四个分担值的亚纯函数的密指量的相对增长性,证明了对于C中的判别的非常数亚纯函数(fz),g(z),如果aj(j=1,2,3,4)为其判别的分担值,其中a4是其CM分担值,且■λ>2/3,ER+,mesE<+∞且(r,f)>λT(r,f)(r■E),则有(2/3+o(1))Σ(N(r,g=aj) j from 1 to 4)≤Σ(N(r,f=aj) j from 1 to 4)≤(2/3+o(1))Σ(N(r,g=aj) j from 1 to 4)(r■E;r→∞)。 相似文献
9.
讨论了单位圆盘上的一类积分算子诱导的复动力系统.设f（z）是在单位圆盘（D={︱z︱≤1}）上满足f（0）=0的解析函数,定义复Volterra型算子为（If）（z）=∫0zf（t）dt.研究迭代算子（Jf）（z）=（If）（z）/‖If‖∞的性质,得到对任意n,使得Jnf（z）在边界D上一点z0存在唯一不动点的充分必要条件. 相似文献
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11.
设(F)为定义在区域D内的一族亚纯函数,a(z)和b(z)为两个在D满足a(z)≠b(z)和a(z)≠b(k)(z)以及a(z)(≠)a'(z)的全纯函数,若对于任意的f∈(F),f(z)-a(z)的零点重级至少是k,f(z)和f(k)(z)分担a(z),且当f(z)=b(z)时,f(k)(z)=b(z),那么(F)在... 相似文献
12.
林珊华 《泉州师范学院学报》2010,28(2):1-5
采用权弱分担值的思想讨论两个亚纯函数fnf′,gng′权弱分担有理函数的唯一性,得到：设p（z）,q（z）为两个互质的n1,n2次多项式,f,g为两个非常数超越亚纯函数,如果fnf′与gng′分担＂（pq（（zz））,m）＂且（1）当2≤m≤∞时,满足n≥max{11,2n1＋4n2＋3};（2）当m=1时,满足n≥max{13,2n1＋4n2＋3};（3）当m=0时,满足n≥max{23,2n1＋4n2＋3},则f=c1Q（z）exp（α（z））,g=c2Q-1（z）exp（-α（z））,其中：c1,c2为2个常数且Q（z）是有理函数;α（z）为满足（c1c2）n＋1（Q′（z）/Q（z）＋α′（z））2≡（p（z）/q（z））2的多项式,或者f=tg,t为常数且满足tn＋1=1. 相似文献
13.
利用Pang-Zalcman方法研究全纯函数微分多项式不取例外函数,得到了如下的正规定则:设■是区域D内的全纯函数族,对于任意的f∈■,f的零点重级至少是k+1,且满足L(z)≠z,其中L(z)=f(k)(z)+a1(z)f(k-1)(z)+…+ak(z)f(z)为f的微分多项式,ai(z)(i=1,2,…,k,k≥1)在D内解析,那么■在D内正规. 相似文献
14.
吴新生 《安徽广播电视大学学报》2001,(1):67-77
In the paper: the representation of large even integer as a sum of two primes is proved to be right independently by each of W-progression ∑∞n=1(1)/((n+1)(n-1)!)of the discovery and the prime theorem. It is induced as two following problems which are solved for getting results of ration: Is there a function of f(2n) to be only dependent upon 2n or not? And it can express a number of group of prime solutions on representation of even integer as a sum of two primes. In one－dimensional space, the prime theorem is led into odd sequence integer to find P(G)～(2 )/(log n).P(G) is regarded as a data handling tool for setting a mathematical model of random sampling, get: P2n(1，1)n＞22n-P2=P1=f(2n)～(2nlogn/2)/(log2nlog2n)(2n→∞). The prime theorem π(x) is generalized to the two-dimensional space: π(x,y). A mathematical model of average values is set up by π(x,y), get: P2n(1，1)2n＞22n=P1+P2=f(2n)2～(2n)/(log22n)(2n→∞). But for expressing a number of group of prime solutions of even integer，the laws of values of principal steps of the two different functions f(2n) and f(2n)2 are unanimous. Thus, the proof of different ways lead to the same result and determines a forceful declaration: Goldbach’s conjecture is proved to be a right theorem. 相似文献
15.
林珊华 《泉州师范学院学报》2011,29(2):37-42,54
从权弱分担的角度分析亚纯函数（或整函数）fn与其k阶导数[fn]（k）的唯一性问题,得到f（n）=[fn]（k）且f=cexp（（λ/n）z）（c为非需常数,λk=1）的充分条件. 相似文献
16.
徐能 《常熟理工学院学报》2005,19(2):11-14
设An(p)(p,n∈N={1,2,3,…})表示f(z)=zp+ap+nzp+n+…一类函数,这类函数在单位圆盘E={z;|z|＜1}上是解析的.利用微分从属的方法得到了单位圆盘内p-叶星形函数的某些充分条件. 相似文献
17.
探讨了复合解析函数零点阶数的计算,证明了当z=z0是f(z)的m阶零点,ξ0=f(z0)是g(ξ)的n阶零点,则z0是复合函数w=g[f(z)]的m·n阶零点,并结合实例阐述了这种方法的简便性. 相似文献
18.
QIAO Lei 《重庆大学学报(英文版)》2007,6(2):146-150
Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem. 相似文献
19.
证明了非常数的亚纯函数的一类非线性微分多项式具有一个非零公共值的亚纯函数的唯一性,其文结果改进了杨重骏和华歆厚的结果,扩充了方明亮的结果。 相似文献
20.
杨逢建 《湖南师范大学教育科学学报》1998,(2)
本文证明了在简单曲线上处处解析的函数在此曲线上存在原函数,由此证明了强可积的条件和Cauchy积分定理、复合闭路定理的条件可在一定范围内得到简化,并给出了相应的积分计算公式与留数计算公式． 相似文献