Weighted statistical convergence and its application to Korovkin type approximation theorem

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• 作者：Mohammad Mursaleen^a ; ^{mursaleenm@gmail.com} ; Vatan Karakaya^b ; ^{vkkaya@yildiz.edu.tr} ; Mü ; zeyyen Ertü ; rk^c ; ^{merturk3263@gmail.com} ; Faik Gü ; rsoy^c ; ^{faikgursoy02@hotmail.com}
• 关键词：Density ; Statistical convergence ; Weighted statistical convergence ; Statistical summability ; Positive linear operator ; Korovkin type approximation theorem
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：15 May, 2012
• 年：2012
• 卷：218
• 期：18
• 页码：9132-9137
• 全文大小：184 K

文摘

The concept of weighted statistical convergence was introduced and studied by Karakaya and Chishti (2009) . In this paper, we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability due to Moricz and Orhan (2004) . We apply this new summability method to prove a Korovkin type approximation theorem by using the test functions . We apply the classical Baskakov operator to construct an example in support of our result.