Summation-Integral Type Operators Based on Lupas-Jain Functions
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Authors: N. MANAV AND N. ISPIR
DOI: 10.46793/KgJMat2102.309M
Abstract:
We introduce a genuine summation-integral type operators based on Lupaş-Jain type base functions related to the unbounded sequences. We investigated their degree of approximation in terms of modulus of continuity and ????-functional for the functions from bounded and continuous functions space. Furthermore, we give some theorems for the local approximation properties of functions belonging to Lipschitz class. Also, we give Voronovskaja theorem for these operators.
Keywords:
Lupaş-Jain functions, summation-integral type operators, moduli of continuity, ????-functional, Voronovskaja theorem.
References:
[1] O. Agratini, On the rate of convergence of a positive approximation process, Nihonkai Math. J. 11 (2000), 47–56.
[2] A. Erençin and F. Taşdelen, On a family of linear and positive operators in weighted spaces, Journal of Inequalities in Pure and Applied Mathematics 8(6) (2007), 2–39.
[3] A. Erençin and F. Taşdelen, On certain Kantorovich type operators, Fasc. Math. 41 (2009), 65–71.
[4] N. K. Govil, V. Gupta, and D. Soybaş, Certain new classes of Durrmeyer type operators, Appl. Math. Comput. 225 (2013), 195–203.
[5] V. Gupta and G. C. Greubel, Moment Estimations of new Szász-Mirakyan-Durrmeyer operators, Appl. Math. Comput. 271 (2015), 540–547.
[6] V. Gupta and G.Tachev, Approximation with Positive Linear Operators and Linear Combinations, Springer, Cham, 2017.
[7] V. Gupta and R. P. Agarwal, Convergence Estimates in Approximation Theory, Springer, USA, New York, 2014.
[8] N. Ispir and N. Manav, Approximation by the summation integral type operators based on Lupaş-Szász basis functions, Journal of Science and Art 4(45), 2018, 853–868.
[9] G. C. Jain, Approximation of functions by a new class of linear operators, J. Aust. Math. Soc. 13(3) (1972), 271–276.
[10] B. Lenze, Bernstein-Baskakov-Kantorovich operators and Lipschitz-type maximal functions, Colloq. Math. Soc. János Bolyai 58 (1990), 469–496.
[11] A. Lupaş, The approximation by some positive linear operators, in: M. W. Müller et al., (Eds.), Proceedings of the International Dortmund Meeting on Approximation Theory, Akademie Verlag, Berlin, 1995, 201–229.
[12] M. A. Özarslan and O. Duman, Local approximation behavior of modified SMK operators, Miskolc Math. Notes 11(1) (2010), 87–89.
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