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Keywords:
q-analogue Baskakov operators; q-Durrmeyer operators; rate of convergence; weighted approximation
q-analogue Baskakov operators; q-Durrmeyer operators; rate of convergence; weighted approximation
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.
References:
[1] Aral, A., Gupta, V.: Generalized q-Baskakov operators. Math. Slovaca 61, 4 (2011), 619–634. DOI 10.2478/s12175-011-0032-3 | MR 2813872 | Zbl 1265.41050
[2] Aral, A., Gupta, V.: On the Durrmeyer type modification of the q-Baskakov type operators. Nonlinear Anal. 72 (2010), 1171–1180. DOI 10.1016/j.na.2009.07.052 | MR 2577517 | Zbl 1180.41012
[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
[4] Sharma, H.: Note on approximation properties of generalized Durrmeyer operators. Mathematical Sciences 6, 1:24 (2012), 1–6. DOI 10.1186/2251-7456-6-24 | MR 3002753 | Zbl 1264.41017
[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. DOI 10.1186/2251-7456-6-26 | MR 3030364 | Zbl 1264.41018
[6] Burgin, M., Duman, O.: Approximations by linear operators in spaces of fuzzy continuous functions. Positivity 15 (2011), 57–72. DOI 10.1007/s11117-009-0041-4 | MR 2782747 | Zbl 1222.41031
[7] Orkcu, M., Dorgu, O.: Statistical approximation of a kind of Kantorovich type q-Szász–Mirakjan operators. Nonlinear Anal. 75, 5 (2012), 2874–2882. DOI 10.1016/j.na.2011.11.029 | MR 2878482
[8] Deo, N.: Faster rate of convergence on Srivastava-Gupta operators. Appl. Math. Compute. 218 (2012), 10486–10491. DOI 10.1016/j.amc.2012.04.012 | MR 2927065 | Zbl 1259.41031
[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. DOI 10.1016/j.amc.2007.12.056 | MR 2431957
[10] Deo, N., Bhardwaj, N., Singh, S. P.: Simultaneous approximation on generalized Bernstein–Durrmeyer operators. Afr. Mat. 24, 1 (2013), 77–82. DOI 10.1007/s13370-011-0041-y | MR 3019807 | Zbl 1263.41010
[11] Duman, O., Orhan, C.: Statistical approximation by positive linear operators. Studia Math. 161 (2006), 187–197. DOI 10.4064/sm161-2-6 | MR 2033235
[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
[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.
[14] Acar, T., Aral, A., Gupta, V.: Rate of convergence for generalized Szász operators. Bull. Math. Sci. 1 (2011), 99–113. DOI 10.1007/s13373-011-0005-4 | MR 2823789 | Zbl 1255.41001
[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.
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