Korovkin type approximation theorems proved via -statistical convergence
- Autores: Hüseyin Aktuglu
- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 259, Nº 1, 2014, págs. 174-181
- Idioma: inglés
- DOI: 10.1016/j.cam.2013.05.012
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Resumen
The concept of statistical convergence was introduced by H. Fast, and studied by various authors. Recently, by using the idea of statistical convergence, M. Balcerzak, K. Dems and A. Komisarski introduced a new type of convergence for sequences of functions called equistatistical convergence. In the present paper we introduce the concepts of áâ-statistical convergence and áâ-statistical convergence of order ã . We show that áâ-statistical convergence is a non-trivial extension of ordinary and statistical convergences. Moreover we show that áâ-statistical convergence includes statistical convergence, ë-statistical convergence, and lacunary statistical convergence. We also introduce the concept of áâ- equistatistical convergence which is a non-trivial extension of equistatistical convergence.
Moreover, we prove that áâ-equistatistical convergence lies between áâ-statistical pointwise convergence and áâ-statistical uniform convergence. Finally we prove Korovkin type approximation theorems via áâ-statistical uniform convergence of order ã and áâ- equistatistical convergence of order ã .
