Korovkin type theorem for sequences of operators depending on a parameter

• Autorzy: Finta Z.

Identyfikatory

DOI

10.1515/dema-2015-0027

• Języki publikacji: EN

Abstrakty

EN

We establish necessary and sufficient conditions for a parameter depending sequence (Ln,λ)n≥1 of positive linear operators such that (Ln,λ)n≥1 converges in the strong operator topology to its limit operator. Some applications of our theorem are also presented.

Słowa kluczowe

EN

Korovkin’s theorem; q-integers; q-Bernstein operators; modulus of smoothness; K-functionals

PL

twierdzenie Korovkina; operatory Bernsteina; moduł gładkości; funkcjonały

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 3
• Strony: 391--403
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Finta Z.

• Babeş-Bolyai University, Department of Mathematics, 1, M. Kogălniceanu St., 400084 Cluj-Napoca, Romania

Bibliografia

• [1] R. A. DeVore, G. G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
• [2] Z. Finta, Note on a Korovkin-type theorem, J. Math. Anal. Appl. 415 (2014), 750–759.
• [3] V. Gupta, Some approximation properties of q-Durrmeyer operators, Appl. Math. Comput. 197 (2008), 172–178.
• [4] A. Il’inskii, S. Ostrovska, Convergence of generalized Bernstein polynomials, J. Approx. Theory 116 (2002), 100–112.
• [5] V. Kac, P. Cheung, Quantum Calculus, Springer-Verlag, New York, 2002.
• [6] A. Lupaş, A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus 9 (1987), 85–92.
• [7] N. I. Mahmudov, P. Sabancigil, Approximation theorems for q-Bernstein-Kantorovich operators, Filomat 27 (2013), 721–730.
• [8] H. Oruç, G. M. Phillips, A generalization of the Bernstein polynomials, Proc. Edinb. Math. Soc. 42 (1999), 403–413.
• [9] G. M. Phillips, Bernstein polynomials based on the q-integers , Ann. Numer. Math. 4 (1997), 511–518.
• [10] T. Trif, Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Numér. Théor. Approx. 29 (2000), 221–229.
• [11] H. Wang, Korovkin-type theorem and application, J. Approx. Theory 132 (2005), 258–264.
• [12] H. Wang, F. Meng, The rate of convergence of q-Bernstein polynomials for 0 < q < 1, J. Approx. Theory 136 (2005), 151–158.