| تعداد نشریات | 24 |
| تعداد شمارهها | 917 |
| تعداد مقالات | 8,230 |
| تعداد مشاهده مقاله | 16,274,827 |
| تعداد دریافت فایل اصل مقاله | 13,752,264 |
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 | ||
|
[1] Fridy, J. A. (1985). On statistical convergence. Analysis, 5, 301-313.
[2] Fridy, J. A. & Orhan, C. (1993). Lacunary statistical convergence. Pacific J. Math., 160, 43-51.
[3] Mursaleen, M. & Alotaibi, A. (2011). Statistical lacunary summability and a Korovkin type approximation theorem. Ann. Univ. Ferrara, 57(2), 373-381.
[4] Korovkin, P. P. (1953). Convergence of linear positive operators in the spaces of continuous functions (Russian). Doklady Akad. Nauk. SSSR (N.S.). 90, 961-964.
[5] Korovkin, P. P. (1960). Linear Operators and Approximation Theory. Delhi. Hindustan Publ. Corp.
[6] Anastassiou, G. A., Mursaleen, M. & Mohiuddine, S. A. (2011). Some approximation theorems for functions of two variables through almost convergence of double sequences. Jour. Comput. Analy. Appl., 13(1), 37-40.
[7] Mohiuddine, S. A. (2011). An application of almost convergence in approximation theorems. Appl. Math. Lett., 24, 1856-1860.
[8] Patterson, R. & Savas, E. (2005). Korovkin and Weierstass approximation via lacunary statistical sequences. J. Math. Stat., 1(2), 165-167.
[9] Edely, O. H. H., Mohiuddine, S. A. & Noman, A. K. (2010). Korovkin type approximation theorems obtained through generalized statistical convergence. Appl. Math. Lett., 23, 1382-1387.
[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.
[15] Boyanov, B. D. & Veselinov, V. M. (1970). A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. Roum., 14(62) 9-13.
[16] Becker, M. (1978). Global approximation theorems for Szasz-Mirakjan and Baskakov operators in polynomial weight spaces. Indiana Univ. Math. J., 27(1), 127-142.
[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. | ||
|
آمار تعداد مشاهده مقاله: 4,079 تعداد دریافت فایل اصل مقاله: 2,011 |
||