Lacunary equi-statistical convergence of positive linear operators

• Autorzy: Hüseyin Aktuğlu , Halil Gezer
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Statistical convergence; Lacunary statistical convergence; A-statistical convergence; Equi-statistical convergence; Korovkin type approximation theorem; Order of convergence

Kategorie tematyczne

• 40A05: Convergence and divergence of series and sequences
• 41A36: Approximation by positive operators
• 41A25: Rate of convergence, degree of approximation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 558-567

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Hüseyin Aktuğlu

• Eastern Mediterranean University

autor

Halil Gezer

• Eastern Mediterranean University

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Identyfikatory

DOI

10.2478/s11533-009-0009-4