Lacunary equi-statistical convergence of positive linear operators |
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Authors: | Hüseyin Aktu?lu Halil Gezer |
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Institution: | (1) Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Gazimağusa, Turkey |
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Abstract: | 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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Keywords: | Statistical convergence Lacunary statistical convergence A-statistical convergence Equi-statistical convergence Korovkin type approximation theorem Order of convergence |
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