Relative Hemen Hemen Yakınsaklık ve Yaklaşım Teoremleri
Year 2016,
Volume: 1 Issue: 2, 114 - 122, 31.12.2016
Kamil Demirci
,
Sevda Orhan
,
Burçak Kolay
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.
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.
Relative Almost Convergence and Approximation Theorems
Year 2016,
Volume: 1 Issue: 2, 114 - 122, 31.12.2016
Kamil Demirci
,
Sevda Orhan
,
Burçak Kolay
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.
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.