329 research outputs found
Approximation by Kantorovich type (p,q)-Bernstein-Schurer Operators
In this paper, we introduce a Shurer type genaralization of
(p,q)-Bernstein-Kantorovich operators based on (p,q)-integers and we call it as
(p,q)-Bernstein-Schurer Kantorovich operators. We study approximation
properties for these operators based on Korovkin's type approximation theorem
and also study some direct theorems. Furthermore, we give comparisons and some
illustrative graphics for the convergence of operators to some function.Comment: 13 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1504.05887. text overlap with arXiv:1504.0588
A Dunkl generalization of q-parametric Szasz-Mirakjan operators
In this paper, we construct a linear positive operators q-parametric
Szasz-Mirakjan operators generated by the q-Dunkl generalization of the
exponential function. We obtain Korovkin's type approximation theorem for these
operators and compute convergence of these operators by using the modulus of
continuity. Furthermore, the rate of convergence of the operators for functions
belonging to the Lipschitz class is presented.Comment: 15 page
Some approximation properties of bivariate Bleimann-Butzer and Hahn operators based on (p,q)-integers
Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and
introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we
construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn
operators based on (p,q)-integers and obtain Korovkin type approximation
theorem of these operators. Furthermore, we compute the rate of convergence of
the operators by using the modulus of continuity and Lipschitz type
maximalfunctions.Comment: 13 page
Some approximation results on higher order generalization of Bernstein type operators defined by (p,q)-integers
In this paper, we introduce the higher order generalization of Bernstein type
operators defined by (p,q)-integers. We establish some approximation results
for these new operators by using the modulus of continuity.Comment: 12 page
On approximation by Stancu type q-Bernstein-Schurer-Kantorovich operators
In this paper we introduce the Stancu type generalization of the
q-Bernstein-Schurer-Kantorovich operators and examine their approximation
properties. We investigate the convergence of our operators with the help of
the Korovkin's approximation theorem and examine the convergence of these
operators in the Lipschitz class of functions. We also investigate the
approximation process for these operators through the statistical Korovkin's
approximation theorem. Also, we present some direct theorems for these
operators. Finally we introduce the bivariate analogue of these operators and
study some results for the bivariate case.Comment: 1
On statistical approximation properties of on statistical approximation properties of (p,q)-bleimann-butzer-hahn operators
The aim of this paper is to introduce a generalization of the
(p,q)-Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain
Korovkin's type statistical approximation theorem for these operators. Also, we
establish the rate of convergence of these operators using the modulus of
continuity. Furthermore, we introduce (p,q)-Bleimann-Butzer-Hahn bivariate
operators.Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1505.0039
Approximation by generalized Szasz operators involving Sheffer polynomials
The purpose of this article is to give a Chlodowsky type generalization of
Szasz operators defined by means of the Sheffer type polynomials. We obtain
convergence properties of our operators with the help of Korovkin's theorem and
the order of convergence by using a classical approach, the second order
modulus of continuity and Peetre's K-functional. Moreover, we study the
convergence of these operators in a weighted space of functions on a positive
semi-axis and estimate the approximation by using a new type of weighted
modulus of continuity introduced by Gadjiev and Aral in [12]. An algorithm is
also given to plot graphical examples, and we have shown the convergence of
these operators towards the function and these examples can be take as a
comparison between the new operators with the previous one too. Finally, some
numerical examples are also given.Comment: 14 pages, 4 figures and 2 table
Approximation by Meyer-Konig and Zeller Operators using (p, q)-CALCULUS
In this paper, we introduce a generalization of the -Meyer-Konig and
Zeller operators by means of the -integers as well as of the
-Gaussian binomial coefficients. For the sequence of
the -Meyer-Konig and Zeller operators denoted by and some
results based on statistical convergence and direct theorems is obtained.
Furthermore, we show comparisons and some illustrative graphics for the
convergence of operators to a function.Comment: 11 pages, 5 figures, title changed, new results adde
Approximation by (p,q)-Lorentz polynomials on a compact disk
In this paper, we introduce a new analogue of Lorentz polynomials based on
(p,q)-integers and we call it as (p,q)-Lorentz polynomials. We obtain
quantitative estimate in the Voronovskaja's type thoerem and exact orders in
simultaneous approximation by the complex (p,q)-Lorentz polynomials of degree
n, where q > p > 1 attached to analytic functions in compact disks of the
complex plane.Comment: 13 page
Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers
In this paper, we apply the Hausdorff measure of noncompactness to obtain the
necessary and sufficient conditions for certain matrix operators on the
Fibonacci difference sequence spaces l_{p}(F) and l_{infinite}(F) to be
compact, where 1<=p<infinite
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