ترغب بنشر مسار تعليمي؟ اضغط هنا

A Note on the value distribution of a differential monomial and some normality criteria

83   0   0.0 ( 0 )
 نشر من قبل Bikash Chakraborty
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.



قيم البحث

اقرأ أيضاً

Let $f$ be a transcendental meromorphic function, defined in the complex plane $mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function $T(r,f)$ in terms of the counting function of a homogeneous differential poly nomial generated by $f$. Our result improves and generalizes some recent results.
Let $f$ be a transcendental meromorphic function defined in the complex plane $mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(geq 2), q_{k}(geq 1)$ are $k(geq1)$ non-negative i ntegers. We obtain a quantitative estimation of the characteristic function $T(r, f)$ in terms of $overline{N}left(r,frac{1}{f^{q_{_{0}}}(f^{(k)})^{q_{k}}-1}right)$.par Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., 14, 93-100, 2011) and Karmakar and Sahoo (Results Math., 73, 2018) for a particular class of transcendental meromorphic functions.
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some o f the results of Fang and Zalcman and Chen et al to a great extent.
133 - Tran Van Tan 2020
In [Israel J. Math, 2014], Grahl and Nevo obtained a significant improvement for the well-known normality criterion of Montel. They proved that for a family of meromorphic functions $mathcal F$ in a domain $Dsubset mathbb C,$ and for a positive const ant $epsilon$, if for each $fin mathcal F$ there exist meromorphic functions $a_f,b_f,c_f$ such that $f$ omits $a_f,b_f,c_f$ in $D$ and $$min{rho(a_f(z),b_f(z)), rho(b_f(z),c_f(z)), rho(c_f(z),a_f(z))}geq epsilon,$$ for all $zin D$, then $mathcal F$ is normal in $D$. Here, $rho$ is the spherical metric in $widehat{mathbb C}$. In this paper, we establish the high-dimension
Let $k$ be an arbitrary field. In this note, we show that if a sequence of relatively prime positive integers ${bf a}=(a_1,a_2,a_3,a_4)$ defines a Gorenstein non complete intersection monomial curve ${mathcal C}({bf a})$ in ${mathbb A}_k^4$, then the re exist two vectors ${bf u}$ and ${bf v}$ such that ${mathcal C}({bf a}+t{bf u})$ and ${mathcal C}({bf a}+t{bf v})$ are also Gorenstein non complete intersection affine monomial curves for almost all $tgeq 0$.
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