Rates of strong uniform convergence of nearest neighbor density estimates on any compact set

1990 ◽  
Vol 11 (4) ◽  
pp. 385-393 ◽  
Author(s):  
Zhang Di-xin
Keyword(s):  
Uniform Convergence ◽  
Nearest Neighbor ◽  
Compact Set ◽  
Density Estimates ◽  
Strong Uniform Convergence

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals Representation of a one class function of two variables by bicontinued fractions

2020 ◽  
Vol 27 (2) ◽  
pp. 13
Author(s):  
M.M. Pahirya
Keyword(s):  
Uniform Convergence ◽  
Continued Fractions ◽  
Compact Set ◽  
Class Function ◽  
Function Of Two Variables

Let function $u (z, w) = f (z) h (w)$ be defined on the compact set  $\mathbf{K} \subset \mathbb{C}^2$. We study the problem of representation of functions of this class by the product of two continued fractions, which is called a bicontinued fraction. Some properties of Thiele reciprocal derivatives,  Thiele continued fractions and  regular C-fractions are proved. The possibility of representation of functions of this class by bicontinued fractions is shown. Examples are considered, domains of convergence and uniform convergence of obtained bicontinued fractions to the function are indicated.

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