Meromorphic Functions Sharing One Value with Their Derivatives Concerning the Difference Operator

作     者：Sujoy Majumder 

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.