Korean J. Math.  Vol 22, No 4 (2014)  pp.671-681
DOI: https://doi.org/10.11568/kjm.2014.22.4.671

Statistical convergence for General Beta Operators

Naokant Deo, Mehmet Ali Ozarslan, Neha Bhardwaj


In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators. 


Beta operators, rate of convergence, statistical convergence.

Subject classification

41A25, 41A36.


Full Text:



Deo N., Faster rate of convergence on Srivastava-Gupta operators, Appl. Math. Comput. 218 (21) (2012), 10486–10491. (Google Scholar)

Deo N. and Bhardwaj N., Some approximation results for Durrmeyer operators, Appl. Math. Comput. 217 (2011), 5531–5536. (Google Scholar)

DeVore R. A. and Lorentz G. G., Constructive Approximation, Springer, Berlin 1993. (Google Scholar)

Dirik F., Statistical convergence and rate of convergence of a sequence of positive linear operators, Math. Commun. 12 (2007), 147–153. (Google Scholar)

Divis Z., Asymptotic behavior of Beta transform of a singular function, Publ. Inst. Math.(Beograd)(N.S.) 49 (63) (1991), 104–110. (Google Scholar)

Duman O., Khan M. K. and Orhan C., A-statistical convergence of approximating operators, Math. Inequal. Appl. 6 (4) (2003), 689–699. (Google Scholar)

Gupta V. and Deo N., textitA note on improved estimations for integrated Sz ́asz-Mirakyan operators, Math. Slovaca, 61 (5) (2011), 799–806. (Google Scholar)

Ispir N. and Gupta V., A-statistical approximation by the generalized Kantorovich-Bernstein type rational operators, SEA. Bull. Math. 32 (2008), 87– 97. (Google Scholar)

Khan M. K., Approximation properties of Beta operators, Progress in approximation theory, Academic Press, Boston, MA, (1991), 483–495. (Google Scholar)

King J. P., Positive linear operators which preserve x2, Acta Math. Hungar 99 (2003), 203–208. (Google Scholar)

Lupa ̧s A., Die Folge der Beta operatorem, Dissertation, Universit ̈at Stuttgart, 1972. (Google Scholar)

O ̈zarslanM.A.andAktuˇgluH.,A-statisticalapproximationofgeneralizedSz ́asz- Mirakjan-Beta operators, Appl. Math. Lett. 24 (2011), 1785–1790. (Google Scholar)

O ̈zarslanM.A.andDumanO.,LocalapproximationbehaviorofmodifiedSMK operators, Miskolc Math. Notes 11 (1) (2010), 87–99. (Google Scholar)

O ̈zarslan M. A., Duman O. and Kaanoˇglu C., Rates of convergence of certain King-type operators for functions with derivative of bounded variation, Math. Comput. Modelling 52 (2010), 334–345. (Google Scholar)

Upreti R., Approximation properties of beta operators, J. Approx. Theory 45 (1985), 85–89. (Google Scholar)

Tunca G. B. and Tuncer Y., Some properties of multivariate Beta operators, Fasc. Math. 41 (2009), 31–43. (Google Scholar)


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