Statistical \(e\)-convergence of double sequences and its application to Korovkin-type approximation theorem for functions of two variables. (English) Zbl 1391.41017
Summary: In this paper, we have introduced the concept of statistical \(e\)-convergence and proved some fundamental properties of statistical \(e\)-convergence. In addition, we have introduced strongly \(e\mathrm{--}|C_{10}|\)-summability and examined the relationship between statistical \(e\)-convergence and strongly \(e\mathrm{--}|C_{10}|\)-summability of double sequences. Finally, we investigate a Korovkin-type approximation theorem for double sequences of positive linear operators on the space of all continuous real-valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version.
Keywords:
double sequence space; \(e\)-convergence; statistical \(e\)-convergence; positive linear operator; Korovkin-type approximation theoremReferences:
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