Displaying similar documents to “I-convergence theorems for a class of k-positive linear operators”

Local approximation properties of certain class of linear positive operators via I-convergence

Mehmet Özarslan, Hüseyin Aktuǧlu (2008)

Open Mathematics

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In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.

Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu, Halil Gezer (2009)

Open Mathematics

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In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin...

A Korovkin type approximation theorems via ℐ -convergence

Oktay Duman (2007)

Czechoslovak Mathematical Journal

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Using the concept of ℐ -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

On integral type generalizations of positive linear operators

O. Duman, M. A. Özarslan, O. Doğru (2006)

Studia Mathematica

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We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute the rates of statistical convergence. Furthermore, we deal with the local approximation and the rth order generalization of our operators.