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 $%...
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Amasya University
2024-12-01
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| Series: | Journal of Amasya University the Institute of Sciences and Technology |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4348876 |
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| author | Sevda Yıldız Kamil Demirci Fadime Dirik |
| author_facet | Sevda Yıldız Kamil Demirci Fadime Dirik |
| author_sort | Sevda Yıldız |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-95a803ffd2c5477bbad03d6d9774aca9 |
| institution | OA Journals |
| issn | 2717-8900 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Amasya University |
| record_format | Article |
| series | Journal of Amasya University the Institute of Sciences and Technology |
| spelling | doaj-art-95a803ffd2c5477bbad03d6d9774aca92025-08-20T02:27:41ZengAmasya UniversityJournal of Amasya University the Institute of Sciences and Technology2717-89002024-12-0152798710.54559/jauist.158139036Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergenceSevda Yıldız0https://orcid.org/0000-0002-4730-2271Kamil Demirci1https://orcid.org/0000-0002-5976-9768Fadime Dirik2https://orcid.org/0000-0002-9316-9037SİNOP ÜNİVERSİTESİSİNOP ÜNİVERSİTESİSİNOP ÜNİVERSİTESİIn 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.https://dergipark.org.tr/en/download/article-file/4348876double sequencestatistical convergence$\mathcal{i}_{2}$-statistical convergencekorovkin theoremthe bleimann butzer and hahn operator |
| spellingShingle | Sevda Yıldız Kamil Demirci Fadime Dirik Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence Journal of Amasya University the Institute of Sciences and Technology double sequence statistical convergence $\mathcal{i}_{2}$-statistical convergence korovkin theorem the bleimann butzer and hahn operator |
| title | Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence |
| title_full | Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence |
| title_fullStr | Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence |
| title_full_unstemmed | Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence |
| title_short | Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence |
| title_sort | approximation theorems using the method of mathcal i 2 statistical convergence |
| topic | double sequence statistical convergence $\mathcal{i}_{2}$-statistical convergence korovkin theorem the bleimann butzer and hahn operator |
| url | https://dergipark.org.tr/en/download/article-file/4348876 |
| work_keys_str_mv | AT sevdayıldız approximationtheoremsusingthemethodofmathcali2statisticalconvergence AT kamildemirci approximationtheoremsusingthemethodofmathcali2statisticalconvergence AT fadimedirik approximationtheoremsusingthemethodofmathcali2statisticalconvergence |