Normal Families Concerning Composite Meromorphic Functions And The Uniqueness Of Difference Polynomials

In1920s, The establishment of Nevanlinna theory, has provided the theoreticalbasis and research tool for the study of other theories. The world famousmathematician N.Steinmetz, W. Bergweiler, I. Lain and our country mathematicianYang Le, Xiong Qinglai and Hong-Xun Yi and so on using this theory obtained aseries of outstanding research achievements in uniqueness theory; meanwhile, ourcountry mathematician Qing-lai Xiong, Chuang C.T and so on using this theorystudied the question of normal families, which made our country be in theinternational forefront in the research of the theory of normal families.The dissertation will introduce some research work under the cordial ProfessorXin-Min Li’s guidance, we uses Nevanlinna theory, Zalcman lemma([26],[27])andValiron-mokhon’ko[25]lemma and establish auxiliary function to deal with thesework. The article consists of four chapters.In chapter one, we mainly introduce classical Nevanlinna theory, classicaldifference Nevanlinna theory, normal family theory and some other concept andnotations.In chapter two, we mainly extend the hold condition of a result which satisfymeromorphic function has maximal deficiency sum in Fang[4]’s article, the conditionis extended from finite order to finite hyper-order.In chapter three, we mainly study the question of normal families of meromorphicfunctions concerning composite meromorphic functions and fixed points. The resultswe get will improveFang-Yuan[20]and Chang-Fang-Zalcman[15]’s results.In chapter four, we mainly study the result that when f is a finite ordertranscendental meromorphic function or a finite order transcendental entire function,fnΔηf Phas infinite zero, and the results that if differential polynomial has sharingvalues. extend the corresponding theorems in Laine-Yang[47]and Liu-Yang[49]...