Weighted Approximation by the đ âSzĂĄszâSchurerâBeta Type Operators
Year 2015,
Volume: 28 Issue: 2, 231 - 238, 22.06.2015
Ä°smet YĂŒksel
,
ĂlkĂŒ Dinlemez
Abstract
In this study, we investigate approximation properties of a Schurer type generalization of q-SzĂĄsz-beta type operators. We estimate the rate of weighted approximation of these operators for functions of polynomial growth on the interval [0,â).
References
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- Phillips, G. M.,Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511-518.
- DoÄru, O. and Gupta, V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q -integers, Georgian Math. J. 12 (2005) (3) 415-422.
- DoÄru, O. and Gupta, V., Korovkin-type approximation properties of bivariate âMeyer- König and Zeller operators, Calcolo 43 (1) (2006) 51-63.
- Gupta, V. and Aral, A., Convergence of the âanalogue of SzĂĄsz-beta operators, Appl. Math. Comput., 216 (2) (2010) 374-380.
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- Govil, N. K. and Gupta, V., âBeta-SzĂĄsz-Stancu operators. Adv. Stud. Contemp. Math. 22(1) (2012) 123
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- Aral, A., Gupta, V. and Agarwal, R. P., Applications of q-calculus in operator theory, Springer, New York, 2013.
- Gupta, V., Srivastava, G. S. and Sahai, A., On simultaneous approximation by SzĂĄsz-beta operators, Soochow J. Math. 21(1) (1995) 1-11.
- Gupta V. and Agarwal, R. P., Convergence estimates in approximation theory. Springer, Cham, ISBN: 978-3-319-02764-7 2014.
- Deo, N., Direct result on the Durrmeyer variant of Beta operators. Southeast Asian Bull. Math. 32(2) (2008) 283-290.
- Deo, N., Direct result on exponential-type operators. Appl. Math. Comput. 204(1) (2008) 109-115
- De Vore R. A. and Lorentz, G. G., Constructive Approximation, Springer, Berlin 1993.
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- Ä°spir, N., On modified Baskakov operators on weighted spaces, Turkish J. Math. 25(3) (2001) 355
Year 2015,
Volume: 28 Issue: 2, 231 - 238, 22.06.2015
Ä°smet YĂŒksel
,
ĂlkĂŒ Dinlemez
References
- LupaĆ, A., A âanalogue of the Bernstein operator, Seminar on numerical and statistical calculus, University of Cluj-Napoca 9 (1987) 85-92.
- Phillips, G. M.,Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511-518.
- DoÄru, O. and Gupta, V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q -integers, Georgian Math. J. 12 (2005) (3) 415-422.
- DoÄru, O. and Gupta, V., Korovkin-type approximation properties of bivariate âMeyer- König and Zeller operators, Calcolo 43 (1) (2006) 51-63.
- Gupta, V. and Aral, A., Convergence of the âanalogue of SzĂĄsz-beta operators, Appl. Math. Comput., 216 (2) (2010) 374-380.
- Gupta, V. and Karslı, H., Some approximation properties by Szåsz -Mirakyan-Baskakov- Stancu operators, Lobachevskii J. Math. 33(2) (2012) 175-182.
- YĂŒksel, Ä°., Approximation by âPhillips operators, Hacet. J. Math. Stat. 40 (2011) no. 2, 191-201.
- YĂŒksel,·İ., Direct results on the âmixed summation integral type operators, J. Appl. Funct. Anal. (2) (2013) 235-245.
- Dinlemez, Ă., YĂŒksel ·İ. and Altın, B., A note on the approximation by the âhybrid summation integral type operators, Taiwanese J. Math. 18(3) (2014) 781
- Gupta, V. and Mahmudov, N. I., Approximation properties of the âSzasz-Mirakjan-Beta operators, Indian J. Industrial and Appl. Math. 3(2) (20012) 41-53.
- YĂŒksel, Ä°. and Dinlemez, Ă., Voronovskaja type approximation theorem for âSzĂĄsz-beta operators. Appl. Math. Comput. 235 (2014) 555-559.
- Govil, N. K. and Gupta, V., âBeta-SzĂĄsz-Stancu operators. Adv. Stud. Contemp. Math. 22(1) (2012) 123
- Mahmudov, N. I., âSzĂĄsz operators which preserve x2 . Slovaca 63(5) (2013) 1059-1072
- Dinlemez, Ă., Convergence of the âStancu- Szasz-beta type operators, J. Inequal. Appl. 2014, :354, 8 pp.
- Jackson, F. H., On âdefinite integrals, quart. J. Pure Appl. Math., 41(15) (1910) 193-203.
- Koelink, H. T. and Koornwinder, T. H., âspecial functions, a tutorial, Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990) 141,142, Contemp. Math., 134,
- Amer. Math. Soc., Providence, RI, 1992.
- Kac, V. G. and Cheung, P., Quantum calculus, Universitext. Springer-Verlag, New York, 2002.
- De Sole, A. and Kac, V. G., On integral representations of âgamma and âbeta functions, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 16(1) (2005) 11-29.
- Aral, A., Gupta, V. and Agarwal, R. P., Applications of q-calculus in operator theory, Springer, New York, 2013.
- Gupta, V., Srivastava, G. S. and Sahai, A., On simultaneous approximation by SzĂĄsz-beta operators, Soochow J. Math. 21(1) (1995) 1-11.
- Gupta V. and Agarwal, R. P., Convergence estimates in approximation theory. Springer, Cham, ISBN: 978-3-319-02764-7 2014.
- Deo, N., Direct result on the Durrmeyer variant of Beta operators. Southeast Asian Bull. Math. 32(2) (2008) 283-290.
- Deo, N., Direct result on exponential-type operators. Appl. Math. Comput. 204(1) (2008) 109-115
- De Vore R. A. and Lorentz, G. G., Constructive Approximation, Springer, Berlin 1993.
- Gadzhiev, A. D., Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5) (1976) 786; English Translation, Math. Notes, 20(5/6) (1976) 996-998.
- Ä°spir, N., On modified Baskakov operators on weighted spaces, Turkish J. Math. 25(3) (2001) 355