×

Convergence rate of Szász operators involving Boas-Buck-type polynomials. (English) Zbl 1490.41010


MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Szász, O., Generalization of S. Bernstein’s polynomials to \(n\) the infinite interval, J Res Natl Bur Stand, 45, 239-245 (1950) · Zbl 1467.41005 · doi:10.6028/jres.045.024
[2] Jakimovski, A.; Leviatan, D., Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj), 11, 97-103 (1969) · Zbl 0188.36801
[3] Ismail, MEH, On a generalization of Szász operators, Mathematica (Cluj), 39, 259-267 (1974) · Zbl 0385.41015
[4] Varma, S.; Sucu, S.; Icoz, G., Generalization of Szász Operators involving Brenke type polynomials, Comput Math Appl, 64, 2, 121-127 (2012) · Zbl 1252.41023 · doi:10.1016/j.camwa.2012.01.025
[5] Sucu, S.; İçöz, G.; Varma, S., On some extensions of Szász operators including Boas-Buck type polynomials, Abstr Appl Anal, 680340, 1-15 (2012) · Zbl 1250.41014 · doi:10.1155/2012/680340
[6] Bojanic, R., An estimate of the rate of convergence for Fourier series of functions of bounded variation, Publ Inst Math (Belgrade), 26, 40, 57-60 (1979) · Zbl 0451.42004
[7] Bojanic, R.; Vuilleumier, M., On the rate of convergence of Fourier-Legendre series of functions of bounded variation, J Approx Theory, 31, 67-79 (1981) · Zbl 0494.42003 · doi:10.1016/0021-9045(81)90031-9
[8] Acar, T., Asymptotic formulas for generalized Szász-Mirakyan operators, Appl Math Comput, 263, 233-239 (2015) · Zbl 1410.41025
[9] Acar, T., \((p, q)\)-generalization of Szász-Mirakyan operators, Math Methods Appl Sci, 39, 10, 2685-2695 (2016) · Zbl 1342.41019 · doi:10.1002/mma.3721
[10] Acar, T.; Ulusoy, G., Approximation by modified Szász-Durrmeyer operators, Period Math Hungar, 72, 1, 64-75 (2016) · Zbl 1389.41024 · doi:10.1007/s10998-015-0091-2
[11] Cheng, F., On the rate of convergence of Bernstein polynomials of functions of bounded variation, J Approx Theory, 39, 259-274 (1983) · Zbl 0533.41020 · doi:10.1016/0021-9045(83)90098-9
[12] Cheng, F., On the rate of convergence of Szász-Mirakyan operator of functions of bounded variation, J Approx Theory, 40, 226-241 (1984) · Zbl 0532.41026 · doi:10.1016/0021-9045(84)90064-9
[13] Öksüzer, Ö.; Karsli, H.; Taşdelen, F., Convergence rate of Bézier variant of an operator involving Laguerre polynomials of degree \(n\), AIP Conf Proc, 1558, 1160-1163 (2013) · doi:10.1063/1.4825714
[14] Öksüzer, Ö.; Karsli, H.; Taşdelen, F., Order of approximation by an operator involving biorthogonal polynomials, J Inequal Appl, 121, 1-13 (2015) · Zbl 1312.41023
[15] Öksüzer, Ö.; Karsli, H.; Taşdelen, F., Approximation by a Kantorovich variant of Szász operators based on Brenke-type polynomials, Mediterr J Math, 13, 5, 3327-3340 (2016) · Zbl 1360.41009 · doi:10.1007/s00009-016-0688-6
[16] Öksüzer, Ö.; Karsli, H.; Taşdelen, F., Rate of convergence of the Bézier variant of an operator involving Laguerre polynomials, Math Methods Appl Sci, 41, 3, 912-919 (2018) · Zbl 1384.41014 · doi:10.1002/mma.3705
[17] Pych-Taberska, P.; Karsli, H., On the rates of convergence of Bernstein-Chlodovsky polynomials and their Bézier-type variants, Appl Anal, 90, 3-4, 403-416 (2011) · Zbl 1217.41018 · doi:10.1080/00036810903399046
[18] Zeng, XM, Rates of approximation of bounded variation functions by two generalized Meyer-König and Zeller type operators, Comput Math Appl, 39, 1-13 (2000) · Zbl 0972.41018 · doi:10.1016/S0898-1221(00)00082-1
[19] Grüss, G., Über das Maximum des absoluten Betrages von \(\frac{1}{{b - a}}\int \limits_a^b f(x)g(x)dx - \frac{1}{(b-a)^2}\int \limits_a^b f(x) dx \int \limits_a^b g(x) dx\), (German) Math Z, 39, 1, 215-226 (1935) · JFM 60.0189.02 · doi:10.1007/BF01201355
[20] Acu A M (2016) Approximation by Certain Positive Linear Operators. Habilitation Thesis, Lucian Blaga University of Sibiu, Romania
[21] Acar, T., Quantitative \(q\)-Voronovskaya and \(q\)-GrüssVoronovskaya-type results for \(q\)-Szász operators, Georgian Math J, 23, 4, 459-468 (2016) · Zbl 1351.41020 · doi:10.1515/gmj-2016-0007
[22] Acar, T.; Aral, A.; Rasa, I., The new forms of Voronovskaya’s theorem in weighted spaces, Positivity, 20, 1, 25-40 (2016) · Zbl 1334.41015 · doi:10.1007/s11117-015-0338-4
[23] Acu, AM; Gonska, H.; Rasa, I., Grüss-type and Ostrowski-type inequalities in approximation theory, Ukrainian Math J, 63, 6, 843-864 (2011) · Zbl 1254.41011 · doi:10.1007/s11253-011-0548-2
[24] Gal, SG; Gonska, H., Grüss and Grüss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables, Jaen J Approx, 7, 1, 97-122 (2015) · Zbl 1384.41004
[25] Neer T, Agrawal PN (2017) Quantitative-Voronovskaya and Grüss-Voronovskaya type theorems for Szász-Durrmeyer type operators blended with multiple Appell polynomials. J Inequal Appl 2017, article no. 244 · Zbl 1373.41021
[26] Shiryayev, AN, Probability (1984), New York: Springer, New York · doi:10.1007/978-1-4899-0018-0
[27] İspir, N., On modified Baskakov operators on weighted spaces, Turk J Math, 25, 3, 355-365 (2001) · Zbl 0999.41013
[28] Guo, S., On the rate of convergence of the Integrated Meyer-König and Zeller Operators for Functions of Bounded Variation, J Approx Theory, 56, 245-255 (1989) · Zbl 0677.41023 · doi:10.1016/0021-9045(89)90114-7
[29] Asai, N., Notes on some orthogonal polynomials having the Brenke type generating functions (mathematical aspects of quantum fields and related topics), RIMS Kokyuroku, Kyoto Univ, 2014-10, 41-53 (1921)
[30] Asai, N.; Kubo, I.; Kuo, HH, Generating functions of orthogonal polynomials and Szegő-Jacobi parameters. Probab Math Statist 23 (2), Acta Univ Wratislav No, 2593, 273-291 (2003) · Zbl 1062.42013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.