Uniform approximation of functions by Bernstein-Stancu operators

2015 ◽  
Vol 31 (2) ◽  
pp. 205-212
Author(s):  
ADRIAN HOLHOS ◽  
Keyword(s):  
Uniform Approximation ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Stancu Operators ◽  
Jacobi Weights

For the class of bounded and continuous functions on (0, 1) we give a characterization of the functions which can be uniformly approximated by Bernstein-Stancu operators. We also study the possibility of uniform approximation of unbounded functions by Bernstein-Stancu operators in weighted spaces with Jacobi weights.

scholarly journals Convolution operators on weighted spaces of continuous functions and supremal convolution

2019 ◽  
Vol 199 (4) ◽  
pp. 1547-1569
Author(s):  
T. Kleiner ◽  
R. Hilfer
Keyword(s):  
Continuous Functions ◽  
Weighted Spaces ◽  
Constructive Method ◽  
Convolution Operators ◽  
Linear Combinations ◽  
The Third ◽  
Bounded Set ◽  
Spaces Of Continuous Functions ◽  
Bounded Sets

AbstractThe convolution of two weighted balls of measures is proved to be contained in a third weighted ball if and only if the supremal convolution of the corresponding two weights is less than or equal to the third weight. Here supremal convolution is introduced as a type of convolution in which integration is replaced with supremum formation. Invoking duality the equivalence implies a characterization of equicontinuity of weight-bounded sets of convolution operators having weighted spaces of continuous functions as domain and range. The overall result is a constructive method to define weighted spaces on which a given set of convolution operators acts as an equicontinuous family of endomorphisms. The result is applied to linear combinations of fractional Weyl integrals and derivatives with orders and coefficients from a given bounded set.

Approximation of functions by some exponential operators of max-product type

2019 ◽  
Vol 56 (1) ◽  
pp. 94-102
Author(s):  
Adrian Holhoş
Keyword(s):  
Modulus Of Continuity ◽  
Uniform Approximation ◽  
Product Type ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Rate Of Approximation

Abstract In this paper we study the uniform approximation of functions by a generalization of the Picard and Gauss-Weierstrass operators of max-product type in exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. We extend and improve previous results.

scholarly journals Approximation of functions by Favard-Szász-Mirakyan operators of max-product type in weighted spaces

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2567-2576
Author(s):  
Adrian Holhoş
Keyword(s):  
Modulus Of Continuity ◽  
Uniform Approximation ◽  
Product Type ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Rate Of Approximation

In this paper we study the uniform approximation of functions by Favard-Sz?sz-Mirakyan operators of max-product type in some exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity.

scholarly journals A Characterization of the Existence of a Fundamental Bounded Resolution for the Space Cc(X) in Terms of X

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Juan Carlos Ferrando
Keyword(s):  
Continuous Functions ◽  
Compact Open Topology ◽  
Tychonoff Space ◽  
Bounded Sets

We characterize in terms of the topology of a Tychonoff space X the existence of a bounded resolution for CcX that swallows the bounded sets, where CcX is the space of real-valued continuous functions on X equipped with the compact-open topology.

Wavelet characterization of weighted spaces

2001 ◽  
Vol 11 (2) ◽  
pp. 241-264 ◽  
Author(s):  
J. García-Cuerva ◽  
J. M. Martell
Keyword(s):  
Weighted Spaces
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