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## entrWeighted approximation by the q-Szász-Schurer-beta type operatorsİsmet YÜKSEL1, Ülkü DİNLEMEZ2,♠

#### İsmet YÜKSEL [1] , Ülkü DİNLEMEZ [2]

In this study, we investigate approximation properties of a Schurer type generalization of q-Szász-beta type operators. We estimate the rate of weighted approximation of these operators for functions of polynomial growth on the interval [0,∞).
q-Szász-Schurer-beta operators, q-mixed operators, weighted approximation, rates of approximation.
• Lupaş, A., A −analogue 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.
• Doğru, 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.
• Doğru, O. and Gupta, V., Korovkin-type approximation properties of bivariate −Meyer- König and Zeller operators, Calcolo 43 (1) (2006) 51-63.
• Gupta, V. and Aral, A., Convergence of the −analogue of Szász-beta operators, Appl. Math. Comput., 216 (2) (2010) 374-380.
• Gupta, V. and Karslı, H., Some approximation properties by Szász -Mirakyan-Baskakov- Stancu operators, Lobachevskii J. Math. 33(2) (2012) 175-182.
• Yüksel, İ., Approximation by −Phillips operators, Hacet. J. Math. Stat. 40 (2011) no. 2, 191-201.
• Yüksel,·İ., Direct results on the −mixed summation integral type operators, J. Appl. Funct. Anal. (2) (2013) 235-245.
• Dinlemez, Ü., Yüksel ·İ. and Altın, B., A note on the approximation by the −hybrid summation integral type operators, Taiwanese J. Math. 18(3) (2014) 781
• Gupta, V. and Mahmudov, N. I., Approximation properties of the −Szasz-Mirakjan-Beta operators, Indian J. Industrial and Appl. Math. 3(2) (20012) 41-53.
• Yüksel, İ. and Dinlemez, Ü., Voronovskaja type approximation theorem for −Szász-beta operators. Appl. Math. Comput. 235 (2014) 555-559.
• Govil, N. K. and Gupta, V., −Beta-Szász-Stancu operators. Adv. Stud. Contemp. Math. 22(1) (2012) 123
• Mahmudov, N. I., −Szász operators which preserve x2 . Slovaca 63(5) (2013) 1059-1072
• Dinlemez, Ü., Convergence of the −Stancu- Szasz-beta type operators, J. Inequal. Appl. 2014, :354, 8 pp.
• Jackson, F. H., On −definite integrals, quart. J. Pure Appl. Math., 41(15) (1910) 193-203.
• Koelink, H. T. and Koornwinder, T. H., −special 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 −gamma and −beta 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 Szász-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.
• İspir, N., On modified Baskakov operators on weighted spaces, Turkish J. Math. 25(3) (2001) 355
Birincil Dil en Mathematics Yazar: İsmet YÜKSEL Yazar: Ülkü DİNLEMEZ Yayımlanma Tarihi : 22 Haziran 2015
 Bibtex @ { gujs97865, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, address = {}, publisher = {Gazi Üniversitesi}, year = {2015}, volume = {28}, pages = {231 - 238}, doi = {}, title = {Weighted approximation by the q-Szász-Schurer-beta type operators}, key = {cite}, author = {YÜKSEL, İsmet and DİNLEMEZ, Ülkü} } APA YÜKSEL, İ , DİNLEMEZ, Ü . (2015). Weighted approximation by the q-Szász-Schurer-beta type operators. Gazi University Journal of Science , 28 (2) , 231-238 . Retrieved from https://dergipark.org.tr/tr/pub/gujs/issue/7435/97865 MLA YÜKSEL, İ , DİNLEMEZ, Ü . "Weighted approximation by the q-Szász-Schurer-beta type operators". Gazi University Journal of Science 28 (2015 ): 231-238 Chicago YÜKSEL, İ , DİNLEMEZ, Ü . "Weighted approximation by the q-Szász-Schurer-beta type operators". Gazi University Journal of Science 28 (2015 ): 231-238 RIS TY - JOUR T1 - Weighted approximation by the q-Szász-Schurer-beta type operators AU - İsmet YÜKSEL , Ülkü DİNLEMEZ Y1 - 2015 PY - 2015 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 231 EP - 238 VL - 28 IS - 2 SN - -2147-1762 M3 - UR - Y2 - 2020 ER - EndNote %0 Gazi University Journal of Science Weighted approximation by the q-Szász-Schurer-beta type operators %A İsmet YÜKSEL , Ülkü DİNLEMEZ %T Weighted approximation by the q-Szász-Schurer-beta type operators %D 2015 %J Gazi University Journal of Science %P -2147-1762 %V 28 %N 2 %R %U ISNAD YÜKSEL, İsmet , DİNLEMEZ, Ülkü . "Weighted approximation by the q-Szász-Schurer-beta type operators". Gazi University Journal of Science 28 / 2 (Haziran 2015): 231-238 . AMA YÜKSEL İ , DİNLEMEZ Ü . Weighted approximation by the q-Szász-Schurer-beta type operators. Gazi University Journal of Science. 2015; 28(2): 231-238. Vancouver YÜKSEL İ , DİNLEMEZ Ü . Weighted approximation by the q-Szász-Schurer-beta type operators. Gazi University Journal of Science. 2015; 28(2): 238-231.

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