Statistically Relatively A−summability of Convergence of Double Sequences of Positive Linear Operators

Abstract

In this paper, we introduce the concept of statistically relatively A-summability. Based upon this definition and A-statistically relatively uniform convergence for double sequences of functions, we prove a Korovkin-type approximation theorem and give a strong example. Also, we study the rates of statistical relatively A−summability of positive linear operators.

Keywords

• Statistical relatively convergence,statistical A−summability,the Korovkin theorem,positive linear operatör

References

1. F. Altomare and M. Campiti, Korovkin Type Approximation Theory and Its Application, Walter de Gruyter Publ., Berlin (1994)
2. 2. Anastassiou, G. A. and Duman, O., A Baskakov type generalization of statistical Korovkin theory. J. Math. Anal. Appl. 340, 476-486 (2008)
3. 3. Anastassiou, G. A. and Duman, O., Statistical fuzzy approximation by fuzzy positive linear operators. Compt. Math. Appl. 55, 573-580, (2008)
4. 4. E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15, 197-201 (1914)
5. 5. E. W. Chittenden, On the limit functions of sequences of continuous functions converging relatively uniformly, Transactions of the AMS, 20, 179-184 (1919)
6. 6. E. W. Chittenden, Relatively uniform convergence and classication of functions, Transactions of the AMS, 23, 1-15, (1922)
7. 7. F. Dirik and K. Demirci, Korovkin Type Approximation Theorem for Functions of Two Variables in Statistical Sense, Turk J. Math. 34, 73-83, (2010)
8. 8. Hamilton, H. J., Transformations of multiple sequences, Duke Math. J. 2, 29-60 (1936)

9. 9. G. H. Hardy, Divergent series, Oxford Uni. Press, London, (1949)