Meromorphic Functions Sharing One Value with Their Derivatives Concerning the Difference Operator
作者机构:Department of MathematicsKatwa CollegeBurdwan 713130India Present Address:Department of MathematicsRaiganj UniversityRaiganjWest Bengal 733134India
出 版 物:《Communications in Mathematics and Statistics》 (数学与统计通讯(英文))
年 卷 期:2017年第5卷第4期
页 面:407-427页
核心收录:
学科分类:07[理学] 0714[理学-统计学(可授理学、经济学学位)] 0701[理学-数学] 0812[工学-计算机科学与技术(可授工学、理学学位)] 070101[理学-基础数学]
主 题:Uniqueness Meromorphic function·Shift operator Difference polynomial Sharing values
摘 要:Let f(z)beanon-constantmeromorphicfunctionoffiniteorder,c∈C\{0}andk∈*** f(z)and f(k)(z+c)share1CM(IM),f(z)and f(z+c)share∞*** N(r,0;f)=S(r,f)(N(r,0;f(z))+N(r,0;f(k)(z+c))=S(r,f)),then either f(z)≡f(k)(z+c)or f(z)is a solution of the following equation:f((z+c)−1=a(z)(f(z)−1))f(z)+1 a(z)),and N(r,0;f(z)+1 a(z))=S(r,f)(f′(z+c)−1=a(z)(f(z)−1)(f(z)+1 a(z)))where a(z)(≡−1,0,∞)(a(z)(≡0,∞))is a meromorphic function satisfying T(r,a)=S(r,f).Also we exhibit some examples to show that the conditions of our results are the best possible.