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Start Over Subject modulus of continuity

1. Approximation by $q$-Bernstein type operators

Creator:
Finta, Zoltán
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$q$-integers, $q$-Bernstein operators, the Hahn-Banach theorem, and modulus of continuity
Language:
English
Description:
Using the $q$-Bernstein basis, we construct a new sequence $\{ L_{n} \}$ of positive linear operators in $C[0,1].$ We study its approximation properties and the rate of convergence in terms of modulus of continuity.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Approximation properties for modified (p, q)-Bernstein-Durrmeyer operators

Creator:
Mursaleen, Mohammad and Alabied, Ahmed A. H.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
(p, q)-integer, (p, q)-Bernstein-Durrmeyer operator, q-Bernstein-Durrmeyer operator, modulus of continuity, positive linear operator, and Korovkin type approximation theorem
Language:
English
Description:
We introduce modified (p, q)-Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators D∗ n,p,q and compute the rate of convergence for the function f belonging to the class LipM(γ).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Approximation properties of bivariate complex $q$-Bernstein polynomials in the case $q>1$

Creator:
Mahmudov, Nazim I.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$q$-Bernstein polynomials, modulus of continuity, and Voronovskaja type theorem
Language:
English
Description:
In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate $q$-Bernstein polynomials for a function analytic in the polydisc $D_{R_{1}}\times D_{R_{2}}=\{z\in C\colon \vert z\vert <R_{1}\} \times \{ z\in C\colon \vert z\vert <R_{1}\}$ for arbitrary fixed $q>1$. We give quantitative Voronovskaja type estimates for the bivariate $q$-Bernstein polynomials for $q>1$. In the univariate case the similar results were obtained by S. Ostrovska: $q$-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Extension and reconstruction theorems for the Urysohn universal metric space

Creator:
Kubiś, Wiesław and Rubin, Matatyahu
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Urysohn space, bilipschitz homeomorphism, modulus of continuity, reconstruction theorem, and extension theorem
Language:
English
Description:
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. King type modification of $q$-Bernstein-Schurer operators

Creator:
Ren, Mei-Ying and Zeng, Xiao-Ming
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
King type operator, $q$-Bernstein-Schurer operator, Korovich type approximation theorem, rate of convergence, Voronovskaja-type result, and modulus of continuity
Language:
English
Description:
Very recently the $q$-Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve $x^{2}$ (2003), in this paper we modify $q$-Bernstein-Schurer operators to King type modification of $q$-Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions $x^{2}$ and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

6. On Dyakonov type theorems for harmonic quasiregular mappings

Creator:
Arsenović, Miloš and Pavlović, Miroslav
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, modulus of continuity, harmonic mapping, quasiregular mapping, 13, and 51
Language:
English
Description:
We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc., Miloš Arsenović, Miroslav Pavlović., and Seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public