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5 Demonstratio Mathematica

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Certain generalized q-operators

Prakash O., Sharma D., Maheshwari P.

Demonstratio Mathematica

2015

Vol. 48, nr 3

404--412

The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov–Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov–Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.

Approximation properties of certain summation integral type operators

Patel P., Mishra V. N.

Demonstratio Mathematica

2015

Vol. 48, nr 1

77--90

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

on q-Baskakov type operators

Aral A., Gupta V.

Demonstratio Mathematica

2009

Vol. 42, nr 1

109-122

In the present paper we introduce two q-analogous of the well known Baskakoy operators. For the first operator we obtain convergence property on bounded interval. Then we give the montonity on the sequence of q-Baskakov operators for n when the function f is convex. For second operator, we obtain direct approximation property on unbounded interval and estimate the rate of convergence. One can say that, depending on the selection of q, these operators are more flexible then the classical Baskakov operators while retaining their approximation properties.

About some linear and positive operators defined by infinite sum

Pop O.

Demonstratio Mathematica

2006

Vol. 39, nr 2

377-388

In [13], we study a class of linear and positive operators defined by finite sum. In this paper we demonstrate general properties for a class of linear positive operators denned by infinite sum. By particularization, we obtain statements, the convergence and the evaluation for the rate of convergence in therm of the first modulus of smoothness for the Mirakjan-Favard-Szasz operators, Baskakov operators and Mayer-Konig and Zeiler operators. We don't study the convergence of these operators with the well known theorem of Bohman-Korowkin.

Direct and converse theorems for integral-type operators

Finta Z.

Demonstratio Mathematica

2003

Vol. 36, nr 1

137--147

We establish direct and converse results for integral-type operators defined with the aid of Szasz-Mirakjan operator and Baskakov operator, respectively. Moreover, some applications will be given.