Modified Beta approximating operators of the first and second kind
DOI:
https://doi.org/10.33993/jnaat381-902Keywords:
modified beta distribution of the first kind and of the second kind, modified beta operators, positive linear operatorsAbstract
By using the modified beta distributions of the first kind (MB1) and of the second kind (MB2) we obtain a general class of modified beta first kind operators and modified beta second kind operators.We obtain several positive linear operators as a special case of these modified beta operators.Downloads
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Karsli, H., Rate of convergence of new Gamma type operators for functions with derivatives of bounded variation, Mathematical and Computer Modeling, 45, pp. 617-624, 2007, https://doi.org/10.1016/j.mcm.2006.08.001 DOI: https://doi.org/10.1016/j.mcm.2006.08.001
Karsli, H. and Gupta, V., Rate of pointwise convergence of a new kind of gamma operators for functions of bounded variation, Appl. Math. Lett., 2007, doi:10.1016, https://doi.org/10.1016/j.aml.2006.12.011 DOI: https://doi.org/10.1016/j.aml.2006.12.011
Khan, M.R., Approximation properties of beta operators, in Progress in Approximation Theory, Academic Press, New York, pp. 483-495, 1991.
McDonald, J.B., Some generalized functions for the size distributions of icome, Econometrica, 52, pp. 647-663, 1984, https://doi.org/10.2307/1913469 DOI: https://doi.org/10.2307/1913469
Miheşan, V., Approximation of continuous functions by means of positive linear operators, Ph. D. Thesis, "Babeş-Bolyai" University, Cluj-Napoca, 1997 (in Romanian).
Miheşan, V., On the gamma and beta approximation operators, Gen. Math., 6, pp. 61-64, 1998.
Miheşan, V., The beta approximating operators of first kind, Studia Univ. Babeş-Bolyai, Mathematica, vol. XLIX, 2, pp. 65-77, 2004.
Miheşan, V., The beta approximating operators of second kind, Studia Univ. "Babeş-Bolyai", Mathemativa, vol. XLIX, 2, pp. 79-88, 2004.
Miheşan, V., On the modified beta approximating operators of first kind, Rev. Anal. Numér. Théor. Approx., 33, no. 1, pp. 67-71, 2004, http://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art8
Miheşan, V., On the modified beta approximating operators of second kind, Rev. Anal. Numér. Théor. Approx., 34, no. 2, pp. 13-138, 2005, http://ictp.acad.ro/jnaat/journal/article/view/2005-vol34-no2-art2
Miheşan, V., On a general class of beta approximating operators of first kind, (in press).
Miheşan, V., On a general class of beta approximating operators of second kind, (in press).
Mihram, G.A. and Hultquist, R.A., A bivariate warning-time/failure-time distribution, Journal of the American Statistical Association, 62, pp. 589-599, 1967, https://doi.org/10.1080/01621459.1967.10482931 DOI: https://doi.org/10.1080/01621459.1967.10482931
Totik, V., Uniform approximation by positive operators on infinite interval, Analysis Mathematica, 10, pp. 162-182, 1984, https://doi.org/10.1007/bf02350525 DOI: https://doi.org/10.1007/BF02350525
Upreti, R., Approximation properties of beta operators, J. Approx. Theory, 45, pp. 85-89, 1985, https://doi.org/10.1016/0021-9045(85)90036-x DOI: https://doi.org/10.1016/0021-9045(85)90036-X
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