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Rate of convergence of Szász-beta operators based on q-integers

Gupta P., Agrawal P. N.

Demonstratio Mathematica

2017

Vol. 50, nr 1

130--143

The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

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.