Statistical relative \(\mathcal {A}\)-summation process for double sequences on modular spaces

Original Paper

Abstract

In the present paper, we extend the Korovkin type approximation theorem via statistical relative \(\mathcal {A}\)-summation process onto the double sequences of positive linear operators in a modular space. Then we discuss the reduced results which are obtained by special choice of the scale function and the matrix sequences. We apply our new result to bivariate Bernstein–Kantorovich operators in Orlicz spaces and hence we show that it is stronger than the results obtained previously.

Keywords

Positive linear operators Modular spaces Double sequences Matrix summability Statistical convergence 

Mathematics Subject Classification

41A36 47G10 47B38 46E30 

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Department of MathematicsSinop UniversitySinopTurkey

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