| Title:
|
Some Applications of new Modified q-Szász–Mirakyan Operators (English) |
| Author:
|
PATHAK, Ramesh P. |
| Author:
|
SAHOO, Shiv Kumar |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
71-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper we introducing a new sequence of positive q-integral new Modified q-Szász-Mirakyan Operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on $[0,\infty )$. Weighted statistical approximation theorem, Korovkin-type theorems for fuzzy continuous functions, an estimate for the rate of convergence and some properties are also obtained for these operators. (English) |
| Keyword:
|
q-analogue Baskakov operators |
| Keyword:
|
q-Durrmeyer operators |
| Keyword:
|
rate of convergence |
| Keyword:
|
weighted approximation |
| MSC:
|
41A25 |
| MSC:
|
41A35 |
| idZBL:
|
Zbl 1347.41023 |
| idMR:
|
MR3469692 |
| . |
| Date available:
|
2015-12-21T17:08:42Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144764 |
| . |
| Reference:
|
[1] Aral, A., Gupta, V.: Generalized q-Baskakov operators. Math. Slovaca 61, 4 (2011), 619–634. Zbl 1265.41050, MR 2813872, 10.2478/s12175-011-0032-3 |
| Reference:
|
[2] Aral, A., Gupta, V.: On the Durrmeyer type modification of the q-Baskakov type operators. Nonlinear Anal. 72 (2010), 1171–1180. Zbl 1180.41012, MR 2577517, 10.1016/j.na.2009.07.052 |
| Reference:
|
[3] Kasana, H. S., Prasad, G., Agrawal, P. N., Sahai, A.: Modified Szász operators. In: Proc. of Int. Con. on Math. Anal. and its Appl. Pergamon Press (1985), 29–41. MR 0951655 |
| Reference:
|
[4] Sharma, H.: Note on approximation properties of generalized Durrmeyer operators. Mathematical Sciences 6, 1:24 (2012), 1–6. Zbl 1264.41017, MR 3002753, 10.1186/2251-7456-6-24 |
| Reference:
|
[5] Sharma, H., Aujla, S. J.: A certain family of mixed summation-integral-type Lupas–Phillips–Bernstein operators. Math. Sci. 6, 1:26 (2012), 1–9. Zbl 1264.41018, MR 3030364, 10.1186/2251-7456-6-26 |
| Reference:
|
[6] Burgin, M., Duman, O.: Approximations by linear operators in spaces of fuzzy continuous functions. Positivity 15 (2011), 57–72. Zbl 1222.41031, MR 2782747, 10.1007/s11117-009-0041-4 |
| Reference:
|
[7] Orkcu, M., Dorgu, O.: Statistical approximation of a kind of Kantorovich type q-Szász–Mirakjan operators. Nonlinear Anal. 75, 5 (2012), 2874–2882. MR 2878482, 10.1016/j.na.2011.11.029 |
| Reference:
|
[8] Deo, N.: Faster rate of convergence on Srivastava-Gupta operators. Appl. Math. Compute. 218 (2012), 10486–10491. Zbl 1259.41031, MR 2927065, 10.1016/j.amc.2012.04.012 |
| Reference:
|
[9] Deo, N., Noor, M. A., Siddiqui, M. A.: On approximation by class of new Bernstein type operators. Appl. Math. Compute. 201 (2008), 604–612. MR 2431957, 10.1016/j.amc.2007.12.056 |
| Reference:
|
[10] Deo, N., Bhardwaj, N., Singh, S. P.: Simultaneous approximation on generalized Bernstein–Durrmeyer operators. Afr. Mat. 24, 1 (2013), 77–82. Zbl 1263.41010, MR 3019807, 10.1007/s13370-011-0041-y |
| Reference:
|
[11] Duman, O., Orhan, C.: Statistical approximation by positive linear operators. Studia Math. 161 (2006), 187–197. MR 2033235, 10.4064/sm161-2-6 |
| Reference:
|
[12] Dorgu, O., Duman, O.: Statistical approximation of Meyer–König and Zeller operators based on q-integers. Publ. Math. Debrecen 68 (2006), 199–214. MR 2213551 |
| Reference:
|
[13] Sahoo, S. K., Singh, S. P.: Some approximation results on a special class of positive linear operators. Proc. Math. Soc., B. H. University 24, 4 (2008), 1–9. |
| Reference:
|
[14] Acar, T., Aral, A., Gupta, V.: Rate of convergence for generalized Szász operators. Bull. Math. Sci. 1 (2011), 99–113. Zbl 1255.41001, MR 2823789, 10.1007/s13373-011-0005-4 |
| Reference:
|
[15] Basakov, V. A.: An example of a sequence of linear positive operators in the space of continuous functions. Dokl. Akad. Nauk. 131 (1973), 249–251. |
| . |
