Abstract
Let C(R 2+ ) be a class of continuous functions f on R 2+ . A bivariate extension Ln (f,x,y) of Bleimann-Butzer-Hahn operator is defined and its standard convergence properties are given. Moreover, a local analogue of Voronovskaja theorem is also given for a subclass of C(R 2+ ).
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References
Abel, U., On the Asymptotic Approximation with Bivariate Operators of Bleimann, Butzer, and Hahn, J. Approx. Theory, 97(1999), 181–198.
Adell, J.A., de la Cal, J. and Miguel, M.S., On the Property of Monotonic convergence for Multivariate Bernstein-Type Operators, J. Approx. Theory, 80(1995), 132–137.
Alon, N. and Spencer J. H. The Probabilistic Method, Wiley, New York, 1992.
Berens, H. and DeVore, R., Quantitative Korovkin Theorems for Positive Linear Operators onL p-Spaces, Trans. Amer. Math. Soc., 245(1978), 349–361.
Bleimann, G., Butzer, P.L. and Hahn, L., A Bernstein-Type Operator Approximating Continuous Functions, Indag. Math., 42(1980), 255–262.
Jayasri C. and Sitaraman, Y., On a Bernstein-Type Operator of Bleimann, Butzer and Hahn-I, J. Analysis, 1(1993), 125–137.
Jayasri, C. and Sitaraman, Y., On a Bernstein-Type Operator of Bleimann, Butzer and Hahn, J. Computational and Appl. Math., 47(1993), 267–272.
Johnen, H. and Scherer, K., On the Equivalence of theK-Functional and Moduli of Continuity and Some Applications, in Constructive Theory of Functions of Several Variables, (W. Schempp and K. Zeller, Eds.) pp. 119–140, Lecture Notes in Mathematics, Vol. 571, Springer-Verlag, Berlin, 1977.
Khan, R.A., A Note on a Bernstein-Type Operator of Bleimann, Butzer and Hahn, J. Approx. Theory 53(1988), 295–303.
Lehmann, E.L., Theory of Point Estimation, Wadsworth, California, 1991.
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Khan, R.A. A bivariate extension of Bleimann-Butzer-Hahn operator. Approx. Theory & its Appl. 18, 90–100 (2002). https://doi.org/10.1007/BF02837051
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DOI: https://doi.org/10.1007/BF02837051