Results 271 to 280 of about 228,280 (310)

Convergence with a functional

Siberian Mathematical Journal, 1986
Let S be a locally compact metric space with a measure \(\mu\). Given a function F on \(S\times {\mathbb{R}}^{\ell}\), define a functional \({\mathcal L}_ F\), \[ {\mathcal L}_ F(u)=\int_{S}F(x,u(x))d\mu (x) \] (u maps S to \({\mathbb{R}}^{\ell})\). The results have the following nature.
openaire   +2 more sources

Weak Convergence of a Certain Functional

Theory of Probability & Its Applications, 2002
Summary: We consider the functional \(T_n=(S_1^2+\cdots+S_n^2)/(nV_n^2)\) derived from a sequence \(\{X_n\}_{n\geq 1}\) of independent identically distributed random variables, where \(S_k=X_1+\cdots+X_k\), \(V_n^2=X_1^2+\cdots+X_n^2\). Let \(G\) be the distribution function of the random variable \(\int_{0}^{1}W^2(t) dt\), where \(W(t)\), \(t\in [0,1]\
Kruglov, V. M., Petrovskaya, G. N.
openaire   +1 more source

Convergence of Functions

2011
In many situations we have a sequence of functions f n that converges to some function f and f is not easy to study directly. Can we use the functions f n to get some information about f? For instance, if the f n are continuous, is f necessarily continuous?
openaire   +1 more source

Convergent Extensions of Grid‐Functions

Mathematische Nachrichten, 1988
AbstractIt is well‐known that functions u ϵ Wm,p (Ω) can be extended by a bounded linear operator E to functions Eu ≦ Wm,p(Rn), if Ω is CM‐regular and m ≦ M. Here we prove a corresponding result for grid‐functions with extension operators Eh converging to E and mention some applications.
openaire   +2 more sources

Convergence of Functions

2015
Major convergence concepts for sequences of real-valued functions will be considered in this chapter. We have already met four convergence concepts so far (viz., pointwise, uniform, almost everywhere, and convergence in L p ). These are reviewed and compared in this section.
openaire   +1 more source

On convergence of topological aggregation functions

Fuzzy Sets and Systems, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Completely Convex Functions and Convergence

SIAM Journal on Mathematical Analysis, 1979
A function $f(x)$ is completely convex (c.c.) on $[0,1]$ if $( - 1)^k f^{(2k)} (x) \geqq 0$ for $k \geqq 0$ and all x in $[0,1]$. This paper studies the convergence of the partial sums of the Maclaurin series of the function; in particular, how quickly the partial sums turn into a c.c. function. It is shown that no matter where the series is truncated,
openaire   +2 more sources

CONVERGENCE OF CERTAIN FUNCTIONAL SERIES

Mathematics of the USSR-Izvestiya, 1967
Using the idea of extension of the system of functions {fk(x)} to an orthogonal one, the author establishes some assertions relating to convergence, (C,1)-summability and unconditional convergence almost everywhere of series in the system {fk(x)}.
openaire   +2 more sources

On the Convergence of Sequences of Rational Functions

SIAM Journal on Numerical Analysis, 1967
There are numerous kinds of sequences of rational functions, such as sequences of Pad6 approximants and sequences of rational functions of best approximation on a given point set, where the poles of the individual functions are not known even asymptotically, and no effective methods for their determination are at hand.
openaire   +2 more sources

Convergence Theorems for Set Functions

2002
Edited by E ...
DE LUCIA, PAOLO, E. PAP
openaire   +2 more sources