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

Rate of approximation by new variants of Bernstein-Durrmeyer operators

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].Comment: 21 page

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

Gr\"uss and Gr\"uss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables

The first aim of this paper is to prove a Gr\"uss-Voronovskaya estimate for Bernstein and for a class of Bernstein-Durrmeyer polynomials on $[0, 1]$. Then, Gr\"uss and Gr\"uss-Voronovskaya estimates for their corresponding operators of complex variable on compact disks are obtained. Finally, the results are extended to Bernstein-Faber polynomials attached to compact sets in the complex plane

On approximation properties of Baskakov-Schurer-Szasz operators

In this paper, we are dealing with a new type of Baskakov-Schurer-Szasz operators (\ref{eq1}). Approximation properties of this operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. We study $q$-analogues of Baskakov-Schurer-Sz\'{a}sz operators and it's Stancu generalization. In the last section, we give better error estimations for the operators (\ref{eq2}) using King type approach and obtained weighted statistical approximation properties for operator (\ref{qb})Comment: 1

Approximation properties of (p;q)-variant of Stancu-Schurer operators(Revised)

In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second order modulus of continuity, Peetres K-functional Lipschitz class

Approximation by Meyer-Konig and Zeller Operators using (p, q)-CALCULUS

In this paper, we introduce a generalization of the $q$-Meyer-Konig and Zeller operators by means of the $(p,q)$-integers as well as of the $(p,q)$-Gaussian binomial coefficients. For $0< q < p <= 1,$ the sequence of the $(p,q)$-Meyer-Konig and Zeller operators denoted by $M_n,p,q$ 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 a Kantorovich type q-Bernstein-Stancu operators

In this paper, we introduce a Kantorovich type generalization of q-Bernstein-Stancu operators. We study the convergence of the introduced operators and also obtain the rate of convergence by these operators in terms of the modulus of continuity. Further, we study local approximation property and Voronovskaja type theorem for the said operators. We show comparisons and some illustrative graphics for the convergence of operators to a certain function.Comment: 14 pages, submitte

Polynomial Approximation and ωϕr(f,t)\omega^r_\phi (f,t) Twenty Years Later

About twenty years ago the measure of smoothness $\omega ^r_\phi (f,t)$ was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time

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