Artee Approximation by modified gamma type operators. (English) Zbl 1473.41005 Int. J. Adv. Appl. Math. Mech. 5, No. 4, 12-19 (2018). 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. Reviewer: Zoltán Finta (Cluj-Napoca) Cited in 5 Documents MSC: 41A36 Approximation by positive operators 40A05 Convergence and divergence of series and sequences 41A25 Rate of convergence, degree of approximation Keywords:gamma type operators; modulus of continuity; weighted approximation; Voronovskaja type asymptotic formula; rate of convergence PDFBibTeX XMLCite \textit{Artee}, Int. J. Adv. Appl. Math. Mech. 5, No. 4, 12--19 (2018; Zbl 1473.41005) Full Text: Link References: [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. · Zbl 1123.41015 [41] X.M. Zeng, Approximation properties of Gamma operator, J. Math. Anal. Appl., 311(2) (2005), 389-401. · Zbl 1087.41024 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. 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