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

100%
Özarslan M., Aktuǧlu H.
Open Mathematics
|
2008
|
tom 6
|
nr 2
281-286
EN
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.
2
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I-convergence theorems for a class of k-positive linear operators

100%
Özarslan M.
Open Mathematics
|
2009
|
tom 7
|
nr 2
357-362
EN
In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.
3
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Lacunary equi-statistical convergence of positive linear operators

75%
Aktuğlu H., Gezer H.
Open Mathematics
|
2009
|
tom 7
|
nr 3
558-567
EN
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 theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.
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