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On some new sequence spaces and statistical convergence methods for double sequences

Belen C., Yildirim M.

Demonstratio Mathematica

2014

Vol. 47, nr 3

627--637

In this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods.

Statistical approximation in multivariate modular function spaces

Belen C., Yildirim M.

Commentationes Mathematicae

2011

Vol. 51, [Z] 1

39-53

In this paper, using the concept of A-statistical convergence we prove a Korovkin type approximation theorem in multivariate modular function spaces. Furthermore, giving an example via bivariate operators of Kantorovich type, it is shown that our theorem is stronger than its classical case.