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Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu;  Halil Gezer — 2009

Open Mathematics

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 type approximation...

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

Mehmet Özarslan;  Hüseyin Aktuǧlu — 2008

Open Mathematics

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.

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