SavedAdd your journal

Journals / Sinop Üniversitesi Fen Bilimleri Dergisi / 2016 / Cilt: 1 - Sayı: 2

Relative Almost Convergence and Approximation Theorems

Relative Hemen Hemen Yakınsaklık ve Yaklaşım Teoremleri

Kamil Demirci
Sevda Orhan
Burçak Kolay
Pages
114–122
Publication Date
2016-12-31
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we present some consequences.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new type of almost convergence and using this convergence, we give a Korovkin-type approximation theorem.
📊
Key Findings & Data:Then, we construct an example such that our result is stronger than the results given before.
💡
Conclusion & Impact:Also, we present some consequences.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Relative düzgün hemen hemen yakınsaklık · Korovkin teorem · Hemen hemen yakınsaklık

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.

Özet

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.

🔖

Cite This Article

Demirci, K., Orhan, S., Kolay, B. (2016). Relative Almost Convergence and Approximation Theorems. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 1 - Sayı: 2, 114–122. https://ajindex.com/articles/415155

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  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), 359–367
  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.