Abstract
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.
Keywords
Relative düzgün hemen hemen yakınsaklık Korovkin teorem Hemen hemen yakınsaklık İstatistiksel yakınsaklık
References
- [1] S. Banach, Theòrie des operations linéaries, Warszawa, 1932.
- [2] E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15 (1914), 197-201.
- [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] E. W. Chittenden, Relatively uniform convergence and classi cation of functions, Transactions of the AMS, 23 (1922), 1-15.
- [5] K. Demirci and S. Orhan, Statistically Relatively Uniform Convergence of Positive Linear Operators. Results in Mathematics 69 (2016), 359367.
- [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
- [7] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
- [8] S. Karakus, K. Demirci and O. Duman, Statistical approximation by positive linear operators on modular spaces, Positivity 14 (2010), 321-334.
- [9] P.P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
- [10] G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
- [11] S.A. Mohiuddine, An application of almost convergence in approximation theorems, Appl. Math. Letters 24 (2011), 1856-1860.
- [12] E. H. Moore, An introduction to a form of general analysis, The New Haven Mathematical Colloquium, Yale University Press, New Haven, 1910.
- [13] I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, John Wiley & Sons, Fourt Ed. , New York 1980.
- [14] H. Steinhaus, Sur la convergence ordinaire et la convergence asymtotique, Colloq. Math. 2(1951), 73-74.
- [15] B. Y¬lmaz, K. Demirci, S. Orhan, Relative modular convergence of positive linear operators, Positivity, DOI 10.1007/s11117-015-0372-2.
Abstract
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.
Keywords
Relative uniform almost convergence Korovkin Theorem Almost convergence Statistical convergence
References
- [1] S. Banach, Theòrie des operations linéaries, Warszawa, 1932.
- [2] E. W. Chittenden, Relatively uniform convergence of sequences of functions, Transactions of the AMS, 15 (1914), 197-201.
- [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] E. W. Chittenden, Relatively uniform convergence and classi cation of functions, Transactions of the AMS, 23 (1922), 1-15.
- [5] K. Demirci and S. Orhan, Statistically Relatively Uniform Convergence of Positive Linear Operators. Results in Mathematics 69 (2016), 359367.
- [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
- [7] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
- [8] S. Karakus, K. Demirci and O. Duman, Statistical approximation by positive linear operators on modular spaces, Positivity 14 (2010), 321-334.
- [9] P.P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
- [10] G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
- [11] S.A. Mohiuddine, An application of almost convergence in approximation theorems, Appl. Math. Letters 24 (2011), 1856-1860.
- [12] E. H. Moore, An introduction to a form of general analysis, The New Haven Mathematical Colloquium, Yale University Press, New Haven, 1910.
- [13] I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, John Wiley & Sons, Fourt Ed. , New York 1980.
- [14] H. Steinhaus, Sur la convergence ordinaire et la convergence asymtotique, Colloq. Math. 2(1951), 73-74.
- [15] B. Y¬lmaz, K. Demirci, S. Orhan, Relative modular convergence of positive linear operators, Positivity, DOI 10.1007/s11117-015-0372-2.
Details
| Journal Section | Research Articles |
|---|---|
| Authors | |
| Publication Date | December 31, 2016 |
| Submission Date | July 19, 2016 |
| Published in Issue | Year 2016 Volume: 1 Issue: 2 |
