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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.

Derivatives of a polynomial of best approximation and modulus of smoothness in generalized Lebesgue spaces with variable exponent

Jafarov S. Z.

Demonstratio Mathematica

2017

Vol. 50, nr 1

245--251

The relation between derivatives of a polynomial of best approximation and the best approximation of the function is investigated in generalized Lebesgue spaces with variable exponent. In addition, the relationship between the fractional modulus of smoothness of the function and its de la Vallée-Poussin sums is studied.

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.