Approximation behaviour of the generalized Kantorovich-type operators by multiple generating functions
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The purpose of this study is to investigate approximation behaviour of the generalized Kantorovich-type operators by multiple generating functions. For this aim, rstly, we introduce bivariate gener-alization of Kantorovich-type operators and study their approximation behaviour with the help of a Korovkin type theorem. Secondly, we com-pute the rate of convergence of these operators by means of the modules of continuity and the elements of Lipschitz class. Also, we give the r-th order generalization of these operators. In the last part, we give some applications to the di¤erential equations.
Abstract
The purpose of this study is to investigate approximation behaviour of the generalized Kantorovich-type operators by multiple generating functions. For this aim, rstly, we introduce bivariate gener-alization of Kantorovich-type operators and study their approximation behaviour with the help of a Korovkin type theorem. Secondly, we com-pute the rate of convergence of these operators by means of the modules of continuity and the elements of Lipschitz class. Also, we give the r-th order generalization of these operators. In the last part, we give some applications to the di¤erential equations.
참고문헌 (11)
- A. Altn, "The generalization of Meyer-König and Zeller operators by generating functions", J. Math. Anal. Appl, 312, pp.181~194 (2005)
- A. Altn, "Kantorovich type the generalization of Meyer-König and Zeller operators by generating functions", J. Math. Anal. Appl, 312, pp.181~194 (2005)
- A.Aral, "Approximation properties of Kantorovich extension of Ibragimov-Gadjiev operators", WSEAS Trans. Math, 4(4), pp.474~479 (2005)
- A. Pringsheim, "Zur theoric der zweifach unendlichen Zahlenfolgen", Math. Annalen, 53, pp.289~321 (1900)
- F. Tasdelen, "The generalization of bivariate MKZ operators by multiple generating function", J. Math. Anal. Appl, 331(1), pp.727~735 (2007)
- M.A. Özarslan, "Statistical approximation results for Kantorovich type operators involving some special polynomials", Math. Comp. Mod, 48, pp.388~401 (2008)
- O. Dogru, "On positive operators involving a certain class of generating functions", Stud. Sci. Math. Hugarica, 41(4), pp.415~429 (2004)
- P.P. Korovkin, "Linear operators and approximation theory" (1960), Hindustan Publish Co
- V.I. Volkov, "On the convergence of sequence of linear positive operators in the space of continues functions of two variables", Russian Dokl. Akad. Nauk SSSR, 115, pp.17~19 (1957)
- Z. Finta, "On Approximation by modified Kantorovich polinomials", N.s, 138, pp.3~4 (1999)
- O.Dogru, "Approximation by Kantorovich type generalization of Meyer-König and Zeller operators", Glasnik Mat, (36), pp.311~ (2001)