A Note on the Statistical Approximation Properties of the Modified Discrete Operators

ABSTRACT

In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.

In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.

Cite this paper

R. Canatan, "A Note on the Statistical Approximation Properties of the Modified Discrete Operators,"*Open Journal of Discrete Mathematics*, Vol. 2 No. 3, 2012, pp. 114-117. doi: 10.4236/ojdm.2012.23022.

R. Canatan, "A Note on the Statistical Approximation Properties of the Modified Discrete Operators,"

References

[1] I. Niven, H. S. Zuckerman and H. Montgomery, “An Introduction to the Theory of Numbers,” 5th Edition, Wiley, New York, 1991.

[2] H. Fast, “Sur La Convergence Statistique,” Colloquium Mathematicum, Vol. 2, 1951, pp. 241-244.

[3] O. Do?ru, “On Statistical Approximation Properties of Stancu Type Bivariate Generalization of q-Balazs-Szabados Operators,” Proceedings of International Conference on Numerical Analysis and Approximation Theory, Cluj-Napoca, 5-8 July 2006, pp. 179-194.

[4] O. Do?ru, “On Weighted Approximation of Continuous Functions by Linear Positive Operators on Infinite Intervals,” Mathematica, Vol. 41, No. 1, 1999, pp. 39-46.

[5] O. Do?ru, “Weighted Approximation Properties of Szásztype Operators,” International Journal of Mathematics, Vol. 2, 2002, pp. 889-895.

[6] J. Grof, “Approximation durch Polynome mit Belegfunktionen,”Acta Mathematica Hungarica, Vol. 35, No. 1-2, 1980, pp. 109-116. doi:10.1007/BF01896829

[7] H. G. Lehnhoff, “On a Modified Szász-Mirakjan Operator,” Journal of Approximation Theory, Vol. 42, 1984, pp. 278-282. doi:10.1016/0021-9045(84)90045-5

[8] O. Agratini, “On the Convergence of a Truncated Class of Operators,” Bulletin of the Institute of Mathematics Academia Sinica, Vol. 312, No. 3, 2003, pp. 213-223.

[9] A. D. Gadjiev and C. Orhan, “Some Approximation Theorems via Statistical Convergence,” Rocky Mountain Journal of Mathematics, Vol. 32, No. 1, 2002, pp. 129-138. doi:10.1216/rmjm/1030539612

[1] I. Niven, H. S. Zuckerman and H. Montgomery, “An Introduction to the Theory of Numbers,” 5th Edition, Wiley, New York, 1991.

[2] H. Fast, “Sur La Convergence Statistique,” Colloquium Mathematicum, Vol. 2, 1951, pp. 241-244.

[3] O. Do?ru, “On Statistical Approximation Properties of Stancu Type Bivariate Generalization of q-Balazs-Szabados Operators,” Proceedings of International Conference on Numerical Analysis and Approximation Theory, Cluj-Napoca, 5-8 July 2006, pp. 179-194.

[4] O. Do?ru, “On Weighted Approximation of Continuous Functions by Linear Positive Operators on Infinite Intervals,” Mathematica, Vol. 41, No. 1, 1999, pp. 39-46.

[5] O. Do?ru, “Weighted Approximation Properties of Szásztype Operators,” International Journal of Mathematics, Vol. 2, 2002, pp. 889-895.

[6] J. Grof, “Approximation durch Polynome mit Belegfunktionen,”Acta Mathematica Hungarica, Vol. 35, No. 1-2, 1980, pp. 109-116. doi:10.1007/BF01896829

[7] H. G. Lehnhoff, “On a Modified Szász-Mirakjan Operator,” Journal of Approximation Theory, Vol. 42, 1984, pp. 278-282. doi:10.1016/0021-9045(84)90045-5

[8] O. Agratini, “On the Convergence of a Truncated Class of Operators,” Bulletin of the Institute of Mathematics Academia Sinica, Vol. 312, No. 3, 2003, pp. 213-223.

[9] A. D. Gadjiev and C. Orhan, “Some Approximation Theorems via Statistical Convergence,” Rocky Mountain Journal of Mathematics, Vol. 32, No. 1, 2002, pp. 129-138. doi:10.1216/rmjm/1030539612