Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence
In this study, we utilize the concept of $\mathcal{I}$-statistical convergence for double sequences to establish a general approximation theorem of Korovkin-type for double sequences of positive linear operators $(PLOs)$ mapping from $H_{\omega }\left( X\right) $ to $C_{B}\left( X\right) $ where $%...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Amasya University
2024-12-01
|
| Series: | Journal of Amasya University the Institute of Sciences and Technology |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/4348876 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this study, we utilize the concept of $\mathcal{I}$-statistical convergence for double sequences to establish a general approximation theorem of Korovkin-type for double sequences of positive linear operators $(PLOs)$ mapping from $H_{\omega }\left( X\right) $ to $C_{B}\left( X\right) $ where $% X=\left[ 0,\infty \right) \times \left[ 0,\infty \right) .$ We then present an example that demonstrates the applicability of our new main result in cases where classical and statistical approaches are not sufficient. Furthermore, we compute the convergence rate of these double sequences of positive linear operators by employing the modulus of smoothness. |
|---|---|
| ISSN: | 2717-8900 |