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On the bivariate Baskakov-Durrmeyer type operators

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PL
O operatorach dwóch zmiennych typu Baskakowa-Durrmeyera
Języki publikacji
EN
Abstrakty
EN
In this paper we introduce some linear positive operators of the Baskakov-Durrmeyer type in the space of continuous functions of two variables. The theorems on convergence and the degree of approximation are established.
PL
W artykule definiuje się dodatnie operatory liniowe typu Baskakowa-Durrmeyera w przestrzeni ciągłych funkcji dwóch zmiennych. Formułuje się i dowodzi twierdzenia dotyczące zbieżności oraz rzędu zbieżności.
Rocznik
Strony
85--96
Opis fizyczny
Bibliogr. 22 poz., wz.
Twórcy
autor
  • Institute of Mathematics, Pedagogical University of Cracow
autor
  • Institute of Mathematics, Pedagogical University of Cracow
Bibliografia
  • [1] Anastassiou G.A., Gal S.G., Approximation theory: moduli of continuity and global smoothness preservation, Birkhauser, Boston 2000.
  • [2] Atakut Ç., Büyükyazıcı İ., Serenbay S., Approximation properties of Baskakov-Balazs type operators for functions of two variables, “Miskolc Math. Notes” 16.2/2015, 667–678.
  • [3] Dhingas A., Über einige Identitäten vom Bernstein Types, “Norske Vid. Selsk. Trodheim” 24/1951, 96–97.
  • [4] Erençin A., Durrmeyer type modification of generalized Baskakov operators, “Appl. Math. Comput.” 218/2011, 4384–4390.
  • [5] Gurdek M., Rempulska L., Skorupka M., The Baskakov operators for functions of two variables, “Collect. Math.” 50.3/1999, 289–302.
  • [6] İzgi A., Order of approximation of functions of two variables by new type gamma operators, “General Mathematics” 17.1/2009, 23–32.
  • [7] Kajla A., Ispir N., Agraval P.N., Goyal M., Q-Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables, “Appl. Math. Comput.” 275/2016, 372–385.
  • [8] Krech G., Wachnicki E., Direct estimate for some operators of Durrmeyer type in exponential weighted space, “Demonstratio Math.” 47.2/2014, 336–349.
  • [9] Lorenz G.G., Bernstein Polynomials, Univ. of Toronto Press, Toronto 1953.
  • [10] Malejki R., Wachnicki E., On the Baskakov-Durrmeyer type operators, “Comment. Math.” 54.1/2014, 39–49.
  • [11] Miheşan V., Uniform approximation with positive linear operators generalized Baskakov method, “Automat. Comput. Appl. Math.” 7.1/1998, 34–37.
  • [12] Rempulska L., Graczyk S., On generalized Szász-Mirakjan operators of functions of two variables, “Math. Slovaca” 62.1/2012, 87–98.
  • [13] Skorupka M., On approximation of functions of two variables by some linear positive operators, “Le Matematiche” 50.2/1995, 323–336.
  • [14] Stancu D.D., On certain polynomials of two variables of Bernstein type and some applications of them, “Dokl. Akad. Nauk SSSR” 134.1/1960, 221–233.
  • [15] Taşdelen F., Olgun A., Başcanbaz-Tunca G., Approximation of functions of two variables by certain linear positive operators, “Proceedings of the Indian Academy of Sciences: Mathematical Sciences” 117.3/2007, 387–399.
  • [16] Timan A.F., Theory of Approximation of Functions of a Real Variable, Moscow 1960 [in Russian].
  • [17] Wachnicki E., Approximation by bivariate Mazhar-Totik operators, “Comment. Math.” 50.2/2010, 141–153.
  • [18] Wafi, A., Khatoon S., Direct and inverse theorems for generalized Baskokov operators in polynomial weight space, “An. Ştiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.)” 50.1/2004, 159–173.
  • [19] Wafi, A., Khatoon S., On the order of approximation of functions by generalized Baskakov operators, “Indian J. Pure Appl. Math.” 35.3/2004, 347–358.
  • [20] Walczak Z., On certain modified Szász-Mirakyan operators for functions of two variables, Demonstratio Math.” 33.1/2000, 91–100.
  • [21] Walczak Z., Approximation by some linear positive operators of functions of two variables, “Saitama Math. J.” 21/2003, 23–31.
  • [22] Volkov V.I., On the convergence of sequences of linear positive operators in the space of two variables, “Dokl. Akad. Nauk. SSSR” 115/1957, 17–19.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7059ef9a-6f7f-425c-ae73-2c6b9e751f43
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