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On generalized Baskakov-Durrmeyer-Stancu type operators

Kumar A. S., Finta Z., Agrawal P. N.

Demonstratio Mathematica

2017

Vol. 50, nr 1

144--155

In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

Korovkin type theorem for sequences of operators depending on a parameter

Finta Z.

Demonstratio Mathematica

2015

Vol. 48, nr 3

391--403

We establish necessary and sufficient conditions for a parameter depending sequence (Ln,λ)n≥1 of positive linear operators such that (Ln,λ)n≥1 converges in the strong operator topology to its limit operator. Some applications of our theorem are also presented.

Quantitative estimates for the Lupas q-analogue of the Bernstein operator

Finta Z.

Demonstratio Mathematica

2011

Vol. 44, nr 1

123-130

We establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupas in 1987 and for the approximation properties of the limit Lupas operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems.

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.