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Approximation by modified gamma type operators. (English) Zbl 1473.41005

For a modified Gamma type operator, which preserves the affin functions, the basic convergence theorem, a Voronovskaja type theorem, local approximation, rate of convergence, weighted approximation and pointwise estimation are studied.

MSC:

41A36 Approximation by positive operators
40A05 Convergence and divergence of series and sequences
41A25 Rate of convergence, degree of approximation
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[1] N. Deo, Faster rate of convergence on Srivastava-Gupta operators, Appl. Math. Comput., 218 (2012), 10486-10491. · Zbl 1259.41031
[2] R.A. DeVore, G.G. Lorentz, Constructive Approximation, Springer, Berlin (1993). · Zbl 0797.41016
[3] A.D. Gadjiev, Theorems of the type of P.P. korovkin’s theorems, Matematicheskie Zametki, 20 (5) (1976), 781-786. · Zbl 0383.41016
[4] A.D. Gadjiev, R.O. Efendiyev, E. Ibikli, On Korovkin type theorem in the space of locally integrable functions, Czechoslovak Math. J., 1(128) (2003), 45-53. · Zbl 1013.41011
[5] A. Kumar, Voronovskaja type asymptotic approximation by general Gamma type operators, Int. J. of Mathematics and its Applications, 3(4-B) (2015), 71-78.
[6] A. Kumar, Approximation by Stancu type generalized Srivastava-Gupta operators based on certain parameter, Khayyam J. Math., Vol. 3, no. 2 (2017), pp. 147-159. DOI: 10.22034/kjm.2017.49477 · Zbl 1384.41018
[7] A. Kumar, On approximation by certain integral type operators, Khayyam J. Math. 4, no. 2 (2018), 123-134. DOI: 10.22034/kjm.2018.58555
[8] A. Kumar, General Gamma type operators inLpspaces, Palestine Journal of Mathematics, 7(1) (2018), 73-79. · Zbl 1375.41012
[9] A. Kumar, Vandana, Approximation by genuine Lupa¸s-Beta-Stancu operators, J. Appl. Math. and Informatics, Vol. 36 (2018), No. 1-2, pp. 15-28. https://doi.org/10.14317/jami.2018.015 · Zbl 1388.41016
[10] A. Kumar, Vandana, Some approximation properties of generalized integral type operators, Tbilisi Mathematical Journal, 11 (1) (2018), pp. 99-116. DOI 10.2478/tmj-2018-0007. · Zbl 1384.41013
[11] A. Kumar, Vandana, Approximation Properties of Modified Srivastava-Gupta Operators Based on Certain Parameter, Bol. Soc. Paran. Mat., v. 38 (1) (2020), 41-53. doi:10.5269/bspm.v38i1.36907 · Zbl 1431.41010
[12] A. Kumar, D.K. Vishwakarma, Global approximation theorems for general Gamma type operators, Int. J. Adv. Appl. Math. and Mech., 3(2) (2015), 77-83. · Zbl 1359.41007
[13] A. Kumar, Artee, D.K. Vishwakarma, Approximation properties of general gamma type operators in polynomial weighted space, Int. J. Adv. Appl. Math. and Mech., 4(3) (2017), 7-13. · Zbl 1390.41032
[14] A. Kumar, Artee, D.K. Vishwakarma, Rajat Kaushik, On general Gamma-Taylor operators on weighted spaces, Int. J. Adv. Appl. Math. and Mech., 3(4) (2016), 9-15. · Zbl 1367.41014
[15] A. Kumar, L.N. Mishra, Approximation by modified Jain-Baskakov-Stancu operators, Tbilisi Mathematical Jour · Zbl 1371.41021
[16] A. Kumar, V.N. Mishra, Dipti Tapiawala, Stancu type generalization of modified Srivastava-Gupta operators, Eur. J. Pure Appl. Math., Vol. 10, No. 4 (2017), 890-907. · Zbl 1370.41027
[17] J.P. King, Positive linear operators which preservex2, Acta Math. Hungar., (99) (3) (2003), 203-208. · Zbl 1027.41028
[18] B. Lenze, On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math., (50) (1988), 53-63. · Zbl 0652.42004
[19] V.N. Mishra,Preeti Sharma,Marius Birou,Approximation by Modified Jain-Baskakov Operators, arXiv:1508.05309v2 [math.FA] 9 Sep 2015. · Zbl 1448.41022
[20] V.N.Mishra,K.KhatriandL.N.Mishra,Someapproximationpropertiesofq-Baskakov-BetaStancu type operators, Journal of Calculus of Variations, Volume 2013, Article ID 814824, 8 pages. http://dx.doi.org/10.1155/2013/814824 · Zbl 1298.41039
[21] V.N. Mishra, Rajiv B. Gandhi, Ram N. Mohapatraa, Summation-Integral type modification of S ´zasz-MirakjanStancu operators, J. Numer. Anal. Approx. Theory, vol. 45, no.1 (2016), pp. 27-36. · Zbl 1399.41047
[22] M.A. ¨Ozarslan and H. Aktu ˇglu, Local approximation for certain King type operators, Filomat, 27:1 (2013), 173-181. · Zbl 1458.41008
[23] A. ˙Izgi, Voronovskaya type asymptotic approximation by modified gamma operators, Appl. Math. Comput., 217 (2011), 8061-8067. · Zbl 1222.45009
[24] A. ˙Izgi, I. B ¨uy ¨ukyazici, Approximation and rate of approximation on unbounded intervals, Kastamonu Edu. J. Okt., 11(2) (2003), 451-460(in Turkish).
[25] G. Krech, A note on the paper “Voronovskaja type asymptotic approximation by modified gamma operators”, Appl. Math. Comput., 219 (2013), 5787-5791. · Zbl 1273.45008
[26] G. Krech, Modified Gamma operators inLpspaces, Lith. Math. J., X(x), 20xx (2014). · Zbl 1311.41013
[27] G. Krech, On the rate of convergence for modified Gamma operators, Rev. Un. Mat. Argentina, 55 (2) (2014), 123131. · Zbl 1305.41022
[28] H. Karsli, Rate of convergence of a new Gamma type operators for the functions with derivatives of bounded variation, Math. Comput. Modell, 45(5-6) (2007), 617-624. · Zbl 1165.41316
[29] H. Karsli, On convergence of general Gamma type operators, Anal. Theory Appl., 27(3) (2011), 288-300. · Zbl 1265.41035
[30] H. Karsli, P.N. Agrawal, M. Goyal, General Gamma type operators based onq-integers, Appl. Math. Comput., 251 (2015), 564-575. · Zbl 1328.41007
[31] H. Karsli, V. Gupta, A. Izgi, Rate of pointwise convergence of a new kind of gamma operators for functions of bounded variation, Appl. Math. Letters, 22(4) (2009), 505-510. · Zbl 1176.41022
[32] H. Karsli, M.A. ¨Ozarslan, Direct local and global approximation results for operators of gamma type, Hacet. J. Math. Stat., 39(2) (2010), 241-253. · Zbl 1203.41009
[33] A. Lupas, M. M ¨uller, Approximationseigenschaften der Gammaoperatà ˝uren, Mathematische Zeitschrift, 98 (1967), 208-226. · Zbl 0171.02301
[34] S.M. Mazhar, Approximation by positive operators on infinite intervals, Math. Balkanica, 5(2) (1991), 99-104. · Zbl 0756.41028
[35] L.C. Mao, Rate of convergence of Gamma type operator, J. Shangqiu Teachers Coll., 12 (2007), 49-52. · Zbl 1174.41324
[36] P. Patel and V.N. Mishra, Approximation properties of certain summation integral type operators, Demonstratio Mathematica Vol. XLVIII no. 1, 2015. · Zbl 1312.41024
[37] Preeti Sharma, V.N. Mishra, Weighted Approximation theorem for Choldowsky generalization of theq-FavardSzasz operators, arXiv:1510.03408v1 [math.CA] 7 Oct 2015.
[38] V. Totik, The Gamma operator inLpspaces, Publ. Math., 32 (1985), 43-55. · Zbl 0589.41020
[39] D.K. Vishwakarma, Artee, Alok Kumar, Ajay Kumar, Multivariateq-Bernstein-Schurer-Kantorovich Operators, Journal of Mathematics and System Science, 6 (2016), 234-241. doi: 10.17265/2159-5291/2016.06.002
[40] X.W. Xu, J.Y. Wang, Approximation properties of modified Gamma operator, J. Math. Anal. Appl., 332 (2007), 798813.
[41] X.M. Zeng, Approximation properties of Gamma operator, J. Math. Anal. Appl., 311(2) (2005), 389-401. · Zbl 1087.41024
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