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Fatou, Julia, And Escaping Sets In Holomorphic (Sub)Semigroup Dynamics, Bishnu Hari Subedi, Ajaya Singh
Fatou, Julia, And Escaping Sets In Holomorphic (Sub)Semigroup Dynamics, Bishnu Hari Subedi, Ajaya Singh
Turkish Journal of Mathematics
We investigate under what conditions the Fatou, Julia, and escaping sets of a transcendental semigroup are respectively equal to the Fatou, Julia, and escaping sets of their subsemigroups. We define the partial fundamental set and fundamental set of a holomorphic semigroup, and on the basis of these sets, we prove that the Fatou and escaping sets of a transcendental semigroup $ S $ are nonempty.
Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang
Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang
Turkish Journal of Mathematics
This paper concerns the description of the entire or meromorphic solutions to two certain types of differential-difference equations under some certain conditions. The significance of our results lies in that we find the entire solutions of the second type equation with the form $f=Ae^{Bz}$, where $A,B$ are constants that are completely determined only by coefficients and correlated indices. Our results are accurate in a certain sense and are supplemented by an example. In particular, our results generalize and improve a result of Zhang and Huang, and they are closely related to recent results by Dong and Liao.