A Jensen Inequality for a Family of Analytic Functions
نویسنده
چکیده
We improve an estimate obtained in [Br] for the average number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin provided that the field in a larger neighbourhood is close enough to a linear center. The result follows from a new distributional inequality for the number of zeros of a family of univariate holomorphic functions depending holomorphically on a parameter.
منابع مشابه
Fekete-Szegö Problem of Functions Associated with Hyperbolic Domains
In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...
متن کاملApplication of the Norm Estimates for Univalence of Analytic Functions
By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.
متن کاملA Coefficient Inequality for the Class of Analytic Functions in the Unit Disc
The aim of this paper is to give a coefficient inequality for the class of analytic functions in the unit disc D = {z | |z| < 1}. 1. Introduction. Let Ω be the family of functions ω(z) regular in the disc D and satisfying the conditions ω(0) = 0 and |ω(z)| < 1 for z ∈ D.
متن کاملFekete-Szeg"o problems for analytic functions in the space of logistic sigmoid functions based on quasi-subordination
In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...
متن کاملA Converse of the Jensen Inequality for Convex Mappings of Several Variables and Applications
In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon’s and Rényi’s entropy mappings are also given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001