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Korovkin type aproximation theorem through statistical lacunary summability | ||
| Iranian Journal of Science | ||
| مقاله 1، دوره 37، شماره 2، مرداد 2013، صفحه 99-102 اصل مقاله (167.46 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2013.1498 | ||
| نویسندگان | ||
| M. Mursaleen* ؛ R. Ahmad | ||
| Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India | ||
| چکیده | ||
| Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions and in the space as well as for the functions 1, cos and sin in the space of all continuous 2π-periodic functions on the real line. In this paper, we use the notion of statistical lacunary summability to improve the result of [Ann. Univ. Ferrara, 57(2) (2011) 373-381] by using the test functions in place of and We apply the classical Baskakov operator to construct an example in support of our main result. | ||
| کلیدواژه‌ها | ||
| Statistical convergence؛ statistical lacunary summability؛ positive linear operator؛ Korovkin type approximation theorem | ||
| مراجع | ||
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[10] Mursaleen, M. & Alotaibi, A. (2011). Statistical summability and approximation by de la Vall e-Poussin mean. Appl. Math. Lett., 24, 320-324.
[11] Mursaleen, M., Karakaya, V., Ert rk, M. & G rsoy, F. (2012). Weighted statistical convergence and its application to Korovkin type approximation theorem. Appl. Math. Comput., 218, 9132-9137.
[12] Srivastava, H. M., Mursaleen, M. & Khan, A. (2012). Generalized equi-statistical convergence of positive linear operators and associated approximation theorems. Math. Comput. Modelling, 55, 2040-2051.
[13] Belen, C., Mursaleen, M. & Yildirim, M. (2012). Statistical A-summability of double sequences and a Korovkin type approximation theorem. Bull. Korean Math. Soc., 49(4), 851-861.
[14] Mursaleen, M. & Alotaibi, A. (2012). Korovkin type approximation theorem for functions of two variables through statistical A-summability. Adv. Difference Equ., 2012:65, doi:10.1186/1687-1847-2012-65.
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[17] Srivastava, H. M., Mursaleen, M. & Khan, A. (2012). Generalized equi-statistical convergence of positive linear operators and associated approximation theorems, Math. Comput. Modelling, 55, 2040-2051.
[18] Mohiuddine, S. A., Alotaibi, A. & Mursaleen, M. (2012). Statistical summability (C; 1) and a Korovkin type approximation theorem. Jour. Ineq. Appl., 2012:172, doi:10.1186/1029-242X-2012-172.
[19] Mursaleen, M. & Alotaibi, A. (2013). Korovkin type approximation theorem for statistical A-summability of double sequences. Jour. Comput. Anal. Appl., 15(6), 1036-1045.
[20] Mursaleen, M. & Kilicman, A. (2013). Korovkin second theorem via B-statistical A-summability, Abstract Appl. Anal., Volume 2013, Article ID 598963, 6 pages, doi:10.1155/2013/598963.
[21] Edely, O. H. H., Mursaleen, M. & Khan, A. (2013). Approximation for periodic functions via weighted statistical convergence. Appl. Math. Comput., 219, 8231-8236. | ||
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