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

Yıl 2017, Cilt: 2 Sayı: 1, 59 - 66, 01.07.2017

Fadime Dirik , Pınar Okçu Şahin

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• F. Altomare and M. Campiti, Korovkin Type Approximation Theory and Its Application, Walter de Gruyter Publ., Berlin (1994)
• 2. Anastassiou, G. A. and Duman, O., A Baskakov type generalization of statistical Korovkin theory. J. Math. Anal. Appl. 340, 476-486 (2008)
• 3. Anastassiou, G. A. and Duman, O., Statistical fuzzy approximation by fuzzy positive linear operators. Compt. Math. Appl. 55, 573-580, (2008)
• 4. E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15, 197-201 (1914)
• 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. E. W. Chittenden, Relatively uniform convergence and classication of functions, Transactions of the AMS, 23, 1-15, (1922)
• 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. Hamilton, H. J., Transformations of multiple sequences, Duke Math. J. 2, 29-60 (1936)
• 9. G. H. Hardy, Divergent series, Oxford Uni. Press, London, (1949)