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Some properties of modified Szász-Mirakyan operators in polynomial spaces via the power summability method

Braha Naim L.

Journal of Applied Analysis

2020

Vol. 26, nr 1

79--90

In this paperwe will prove the Korovkin type theorem for modified Szász-Mirakyan operators via Astatistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem.

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.

Statistical approximation for periodic functions

Duman O.

Demonstratio Mathematica

2003

Vol. 36, nr 4

873--878

In this paper we study a Korovkin type approximation theorem for positive linear operators on the space of all 2π-periodic and continuous functions on the whole real axis via A-statistical convergence.