Convergence theorem, convergence rate and convergence speed for continuous real functions
نویسندگان
چکیده
منابع مشابه
A Chebyshev Polynomial Rate-of-Convergence Theorem for Stieltjes Functions
The theorem proved here extends the author's previous work on Chebyshev series [4] by showing that if f(x) is a member of the class of so-called "Stieltjes functions" whose asymptotic power series 2 anx" about x = 0 is such that ttlogjaj _ hm —;-= r, «log n then the coefficients of the series of shifted Chebyshev polynomials on x e [0, a],2b„Tf(x/a), satisfy the inequality 2 . m log | (log |M) ...
متن کاملCentral Limit Theorem and Poisson Convergence 8.1 Rate of Convergence for CLT
There are several ways of proving Central Limit Theorems: 1. Use characteristic or moment generating functions or some distributional transform, or 2. Use moment method to show that the k-th moment converges to the k-th moment of standard Normal for all k > 1, or 3. Use Fixed Point method (e.g., maximizing entropy given fixed mean and variance, zero bias transformation etc.) or 4. Replacement o...
متن کاملOn The Mean Convergence of Biharmonic Functions
Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...
متن کاملStatistical Convergence and Ideal Convergence for Sequences of Functions
Let I ⊂ P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X,M, μ), we obtain a statistical version of the Egorov theorem (when μ(X) < ∞). We show that, in its assertion, equi-statistical convergence...
متن کاملVariational convergence of bivariate functions: lopsided convergence
We explore convergence notions for bivariate functions that yield convergence and stability results for their maxinf (or minsup) points. This lays the foundations for the study of the stability of solutions to variational inequalities, the solutions of inclusions, of Nash equilibrium points of non-cooperative games and Walras economic equilibrium points, of fixed points, of solutions to inclusi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2016
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1602505c