scholarly journals A uniform approximation theorem and its application to moment problems

1964 ◽  
Vol 84 (2) ◽  
pp. 143-153 ◽  
Author(s):  
A. Jakimovski ◽  
M. S. Ramanujan
Keyword(s):  
Uniform Approximation ◽  
Approximation Theorem ◽  
Moment Problems

Max-Product Shepard Approximation Operators

2006 ◽  
Vol 10 (4) ◽  
pp. 494-497 ◽  
Author(s):  
Barnabás Bede ◽  
◽  
Hajime Nobuhara ◽  
János Fodor ◽  
Kaoru Hirota ◽  
...  
Keyword(s):  
Error Estimate ◽  
Approximation Theory ◽  
Uniform Approximation ◽  
Approximation Theorem ◽  
Jackson Type ◽  
Approximation Operators

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.

scholarly journals On constrained uniform approximation

2002 ◽  
Vol 31 (2) ◽  
pp. 103-108
Author(s):  
M. A. Bokhari
Keyword(s):  
Uniform Approximation ◽  
Approximation Theorem ◽  
Weierstrass Approximation Theorem

The problem of uniform approximants subject to Hermite interpolatory constraints is considered with an alternate approach. The uniqueness and the convergence aspects of this problem are also discussed. Our approach is based on work of P. Kirchberger (1903) and a generalization of Weierstrass approximation theorem.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

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