Bikash Chakraborty
Let f be a non-constant meromorphic function and a = a(z) be a small function of f. Under certain essential conditions, we obtained similar type conclusion of Bruck Conjecture, when f and its differential polynomial P[f] shares a with weight l. Our result improves and generalizes a recent result of Li, Yang, and Liu.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Bruck. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et. al [14]. However, our method differs the method of L. Z. Yang et. al [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].
We consider the following conjecture (from Huang, et al): Let $Δ^+$ denote the upper half disc in $\mathbb{C}$ and let $γ= ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic function on $Δ^+$ with continuous extension up to $γ$ such that $F$ maps $γ$ into $\{|\mbox{Im} z|\leq C|\mbox{Re} z|\},$ for some positive $C.$ If $F$ vanishes to infinite order at $0$ then $F$ vanishes identically. We show that given the conditions of the conjecture, either $F\equiv 0$ or there is a sequence in $Δ^+$, converging to $0,$ along which $\mbox{Im} F/\mbox{Re}…
In the paper, we have shown that every entire solution of the differential difference equation $Δ_η^{m}f-Q_1=(Δ_η^{k}f-Q_{2})e^{P}$ satisfy hyper order of $f=$degree of $P$ and using this result we prove differential difference counter part Brück conjecture. Also we have proved differential difference counter part Brück conjecture for the special case of hyper order of $f<\frac{1}{2}$.
In this paper, we prove some uniqueness results which improve and generalize several earlier works. Also, we prove a value distribution result concerning $f^{(k)}$ which provides a partial answer to a question of Fang and Wang [A note on the conjectures of Hayman, Mues and Gol'dberg, Comp. Methods, Funct. Theory (2013)13, 533-543].
In this paper, we prove Huang et al.'s conjecture stated that if $f$ is a holomorphic function on $Δ^+:=\{z\in \mathbb C \colon |z|<1,~\mathrm{Im}(z)>0\}$ with $\mathcal{C}^\infty$-smooth extension up to $(-1,1)$ such that $f$ maps $(-1,1)$ into a cone $Γ_C:=\{z\in \mathbb C\colon |\mathrm{Im} (z)| \leq C|\mathrm{Re} (z)|\}$, for some positive number $C$, and $f$ vanishes to infinite order at $0$, then $f$ vanishes identically. In addition, some regularity properties of the Riemann mapping functions on the boundary and an example concerning Huang et al.'s conjecture are also given.
In this paper, taking the question of Zhang and Lü into the background, we present one theorem which will improve and extend some recent results related to the Brück Conjecture.
Some results on zeros distributions and uniqueness of derivatives of difference polynomials
研究了亚纯函数差分多项式导数的零点分布，给出了一些结果，这些结果可以看作是Hayman猜想\cite{hayman1}的离散类似，也部分回答了\cite [P448]{luolin}中的问题.我们还研究了整函数的差分微分多项式具有一个公共值的唯一性问题。这些定理改进了Luo和Lin的\cite{luolin}的结果以及作者\cite{liuliucao}的一些结果.
The subject of our thesis is the uniqueness theory of meromorphic functions and it is devoted to problems concerning Bruck conjecture, set sharing and related topics. The tool, we used in our discussions is classical Nevanlinna theory of meromorphic functions. In 1996, in order to find the relation between an entire function with its derivative, counterpart sharing one value CM, a famous conjecture was proposed by R. Bruck. Since then the conjecture and its analogous results have been investigated by many researchers and continuous efforts have been put on by them. In our thesis, we have obtai…
In this paper we have mainly focused on the uniqueness of two meromorphic functions under the realm of two shared sets problem with certain restrictions which in turn improve the results of { P. Sahoo and H. Karmakar, Uniqueness theorems related to weighted sharing of two sets, Acta Univ. Sapientiae, Mathematica, 10(2) (2018), 329-339} and {P. Sahoo and A. Sarkar, On the uniqueness of meromorphic functions sharing two sets, Bol. Soc. Mat. Mex., (2019), 1-7}. In particular, pointing out some gaps in the statements of the results in { P. Sahoo and H. Karmakar, Uniqueness theorems related to weig…
On the two conjectures
本文针对整函数与其高阶差分算子共享整函数的唯一性问题展开研究，证实了学者提出的两个相关猜想，辅以示例支撑结论。
In this paper, we investigate the zero distributions of $q$-shift difference-differential polynomials of meromorphic functions with zero-order that extends and generalizes the classical Hayman results of the zeros of differential polynomials to q-shift difference. We also investigate the uniqueness problem of $q$-shift difference-differential polynomials sharing a polynomial value with finite weight.
Uniqueness of entire function concerning derivatives and shifts
本文研究整函数关于导数与平移的唯一性问题，提出两个结果，分别解决了Majumder等人提出的公开问题，并在很大程度上改进推广了Huang和Fang的近期结果。
Uniqueness of entire functions sharing two values with their partial derivative operators
本文利用多复变量正常族理论，扩展了李和伊、卢等人关于整个函数唯一性的结果，并通过例子证明了结果的最优性。
A solution to Berndtsson's problem and uniqueness of twisted KE currents
本文通过解决Berndtsson提出的问题，证明了大上同调类中扭曲Kähler-Einstein流的唯一性猜想，从而解决了该领域的核心难题。
We revisit some uniqueness results for a geometric nonlinear PDE related to the scalar curvature in Riemannian geometry and CR geometry. In the Riemannian case we give a new proof of the uniqueness result assuming only a positive lower bound for Ricci curvature. We apply the same principle in the CR case and reconstruct the Jerison-Lee identity in a more general setting. As a consequence we prove a stronger uniqueness result in the CR case. We also discuss some open problems for further study.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。