Milloux Inequality of E-Valued Meromorphic Function
نویسندگان
چکیده
The main purpose of this paper is to establish the Milloux inequality of E-valued meromorphic function from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. As an application, we study the Borel exceptional values of an E-valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalar-valued function of Singh, Gopalakrishna, and Bhoosnurmath.
منابع مشابه
E-Valued Meromorphic Functions With Maximal Deficiency Sum∗
The purpose of this paper is to discuss the relationship between the characteristic function of an E-valued meromorphic function f and and that of its derivative f ′. Consequently, for a finite order E-valued meromorphic function f with maximal deficiency sum, we obtain that T (r, f ′) ∼ (2 − δ(∞̂, f))T (r, f) as r → +∞. Results are obtained to extend the related results for meromorphic scalar v...
متن کاملHölder continuity of a parametric variational inequality
In this paper, we study the Hölder continuity of solution mapping to a parametric variational inequality. At first, recalling a real-valued gap function of the problem, we discuss the Lipschitz continuity of the gap function. Then under the strong monotonicity, we establish the Hölder continuity of the single-valued solution mapping for the problem. Finally, we apply these resu...
متن کاملCharacteristic Functions and Borel Exceptional Values of E-Valued Meromorphic Functions
and Applied Analysis 3 Let n r, f or n r, ∞̂ denote the number of poles of f z in |z| ≤ r and let n r, a, f denote the number of a-points of f z in |z| ≤ r, counting with multiplicities. Define the volume function associated with E-valued meromorphic function f z by V ( r, ∞̂, f V r, f 1 2π ∫ Cr log ∣∣ ∣ ∣ r ξ ∣∣ ∣ ∣Δ log ∥ ∥f ξ ∥ ∥dx ∧ dy, ξ x iy, V ( r, a, f ) 1 2π ∫ Cr log ∣ ∣ ∣ ∣ r ξ ∣ ∣ ∣ ∣Δ...
متن کاملA Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator
We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.
متن کاملValue Distribution for a Class of Small Functions in the Unit Disk
If f is a meromorphic function in the complex plane, R. Nevanlinna noted that its characteristic function T r, f could be used to categorize f according to its rate of growth as |z| r → ∞. Later H. Milloux showed for a transcendental meromorphic function in the plane that for each positive integer k, m r, f k /f o T r, f as r → ∞, possibly outside a set of finite measure where m denotes the pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
دوره 2014 شماره
صفحات -
تاریخ انتشار 2014