ترغب بنشر مسار تعليمي؟ اضغط هنا

A new proof of entire function sharing three small functions CM with it $n-$ exact difference

181   0   0.0 ( 0 )
 نشر من قبل XiaoHuang Huang
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف XiaoHuang Huang




اسأل ChatGPT حول البحث

In this paper, we study the uniqueness of the difference of meromorphic functions. We give a new proof of the following result: Let $f$ be a transcendental meromorphic function of hyper-order less than $1$, let $eta$ be a non-zero complex number, $ngeq1$, an integer, and let $a,b,c$ be three distinct periodic small functions with period $eta$. If $f$ and $Delta_{eta}^{n}f$ share $a,b,c$ CM, then $fequivDelta_{eta}^{n}f$, which using a different method from cite{gkzz}.

قيم البحث

اقرأ أيضاً

If $f$ is an entire function and $a$ is a complex number, $a$ is said to be an asymptotic value of $f$ if there exists a path $gamma$ from $0$ to infinity such that $f(z) - a$ tends to $0$ as $z$ tends to infinity along $gamma$. The Denjoy--Carleman- -Ahlfors Theorem asserts that if $f$ has $n$ distinct asymptotic values, then the rate of growth of $f$ is at least order $n/2$, mean type. A long-standing problem asks whether this conclusion holds for entire functions having $n$ distinct asymptotic (entire) functions, each of growth at most order $1/2$, minimal type. In this paper conditions on the function $f$ and associated asymptotic paths are obtained that are sufficient to guarantee that $f$ satisfies the conclusion of the Denjoy--Carleman--Ahlfors Theorem. In addition, for each positive integer $n$, an example is given of an entire function of order $n$ having $n$ distinct, prescribed asymptotic functions, each of order less than $1/2$.
78 - Tingbin Cao , Huixin Dai , 2018
This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions of zero order in the complex plane $mathbb{C}$. We give the logarithmic difference lemma, the seco nd fundamental theorem, the defect relation, Picard theorem and five-value theorem in sense of Jackson $q$-difference operator. By using this theory, we investigate the growth of entire solutions of linear Jackson $q$-difference equations $D^{k}_{q}f(z)+A(z)f(z)=0$ with meromorphic coefficient $A,$ where $D^k_q$ is Jackson $k$-th order difference operator, and estimate the logarithmic order of some $q$-special functions.
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
In this paper we shall consider the assymptotic growth of $|P_n(z)|^{1/k_n}$ where $P_n(z)$ is a sequence of entire functions of genus zero. Our results extend a result of J. Muller and A. Yavrian. We shall prove that if the sequence of entire functi ons has a geometric growth at each point in a set $E$ being non-thin at $infty$ then it has a geometric growth in $CC$ also. Moreover, if $E$ has some more properties, a similar result also holds for a more general kind of growth. Even in the case where $P_n$ are polynomials, our results are new in the sense that it does not require $k_nsucceq deg(P_n)$ as usually required.
In this paper we shall consider the growth at infinity of a sequence $(P_n)$ of entire functions of bounded orders. Our results extend the results in cite{trong-tuyen2} for the growth of entire functions of genus zero. Given a sequence of entire func tions of bounded orders $P_n(z)$, we found a nearly optimal condition, given in terms of zeros of $P_n$, for which $(k_n)$ that we have begin{eqnarray*} limsup_{ntoinfty}|P_n(z)|^{1/k_n}leq 1 end{eqnarray*} for all $zin mathbb C$ (see Theorem ref{theo5}). Exploring the growth of a sequence of entire functions of bounded orders lead naturally to an extremal function which is similar to the Siciaks extremal function (See Section 6).
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا