Relative Hemen Hemen Yakınsaklık ve Yaklaşım Teoremleri

Öz

Bu makalede, yeni bir hemen hemen yakınsaklık türü tanıtacağız ve bu yakınsaklığı kullanarak Korovkin tipi yaklaşım teoremi vereceğiz. Daha sonra bizim sonucumuzun önceden verilen sonuçlardan daha güçlü olduğunu gösteren bir örnek vereceğiz. Ayrıca, bazı sonuçlar sunacağız.

Anahtar Kelimeler

• Relative düzgün hemen hemen yakınsaklık,Korovkin teorem,Hemen hemen yakınsaklık,İstatistiksel yakınsaklık

Relative Almost Convergence and Approximation Theorems

Öz

In this paper, we introduce a new type of almost convergence and using this convergence, we give a Korovkin-type approximation theorem. Then, we construct an example such that our result is stronger than the results given before. Also, we present some consequences.

Anahtar Kelimeler

• Relative uniform almost convergence,Korovkin Theorem,Almost convergence,Statistical convergence

Kaynakça

1. [1] S. Banach, Theòrie des operations linéaries, Warszawa, 1932.
2. [2] E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15 (1914), 197-201.
3. [3] E. W. Chittenden, On the limit functions of sequences of continuous functions converging relatively uniformly, Transactions of the AMS, 20 (1919), 179-184.
4. [4] E. W. Chittenden, Relatively uniform convergence and classi…cation of functions, Transactions of the AMS, 23 (1922), 1-15.
5. [5] K. Demirci and S. Orhan, Statistically Relatively Uniform Convergence of Positive Linear Operators. Results in Mathematics 69 (2016), 359–367.
6. [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
7. [7] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
8. [8] S. Karakus, K. Demirci and O. Duman, Statistical approximation by positive linear operators on modular spaces, Positivity 14 (2010), 321-334.

9. [9] P.P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
10. [10] G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
11. [11] S.A. Mohiuddine, An application of almost convergence in approximation theorems, Appl. Math. Letters 24 (2011), 1856-1860.
12. [12] E. H. Moore, An introduction to a form of general analysis, The New Haven Mathematical Colloquium, Yale University Press, New Haven, 1910.
13. [13] I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, John Wiley & Sons, Fourt Ed. , New York 1980.
14. [14] H. Steinhaus, Sur la convergence ordinaire et la convergence asymtotique, Colloq. Math. 2(1951), 73-74.
15. [15] B. Y¬lmaz, K. Demirci, S. Orhan, Relative modular convergence of positive linear operators, Positivity, DOI 10.1007/s11117-015-0372-2.