Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces
In the present work, we establish a quantitative estimate for the perturbed sampling Kantorovich operators in Orlicz spaces, in terms of the modulus of smoothness, defined by means of its modular functional. From the obtained result, we also deduce the qualitative order of approximation, by consider...
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De Gruyter
2024-12-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0090 |
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| author | Costarelli Danilo De Angelis Eleonora Vinti Gianluca |
| author_facet | Costarelli Danilo De Angelis Eleonora Vinti Gianluca |
| author_sort | Costarelli Danilo |
| collection | DOAJ |
| description | In the present work, we establish a quantitative estimate for the perturbed sampling Kantorovich operators in Orlicz spaces, in terms of the modulus of smoothness, defined by means of its modular functional. From the obtained result, we also deduce the qualitative order of approximation, by considering functions in suitable Lipschitz classes. This allows us to apply the above results in certain Orlicz spaces of particular interest, such as the interpolation spaces, the exponential spaces and the Lp{L}^{p}-spaces, 1≤p<+∞1\le p\lt +\infty . In particular, in the latter case, we also provide an estimate established using a direct proof based on certain properties of the Lp{L}^{p}-modulus of smoothness, which are not valid in the general case of Orlicz spaces. The possibility of using a direct approach allows us to improve the estimate that can be deduced as a consequence of the one achieved in Orlicz spaces. In the final part of the article, we furnish some estimates and the corresponding qualitative order of approximation in the space of uniformly continuous and bounded functions. |
| format | Article |
| id | doaj-art-c4a5c5d42c114935bd8a42f98d4683fd |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-c4a5c5d42c114935bd8a42f98d4683fd2025-02-02T15:45:16ZengDe GruyterDemonstratio Mathematica2391-46612024-12-01571295210.1515/dema-2024-0090Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spacesCostarelli Danilo0De Angelis Eleonora1Vinti Gianluca2Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli 1, IT 06123 Perugia, ItalyDepartment of Mathematics and Computer Science “Ulisse Dini”, University of Florence, 67/a Viale Giovanni Battista Morgagni, IT 50134 Florence, ItalyDepartment of Mathematics and Computer Science, University of Perugia, Via Vanvitelli 1, IT 06123 Perugia, ItalyIn the present work, we establish a quantitative estimate for the perturbed sampling Kantorovich operators in Orlicz spaces, in terms of the modulus of smoothness, defined by means of its modular functional. From the obtained result, we also deduce the qualitative order of approximation, by considering functions in suitable Lipschitz classes. This allows us to apply the above results in certain Orlicz spaces of particular interest, such as the interpolation spaces, the exponential spaces and the Lp{L}^{p}-spaces, 1≤p<+∞1\le p\lt +\infty . In particular, in the latter case, we also provide an estimate established using a direct proof based on certain properties of the Lp{L}^{p}-modulus of smoothness, which are not valid in the general case of Orlicz spaces. The possibility of using a direct approach allows us to improve the estimate that can be deduced as a consequence of the one achieved in Orlicz spaces. In the final part of the article, we furnish some estimates and the corresponding qualitative order of approximation in the space of uniformly continuous and bounded functions.https://doi.org/10.1515/dema-2024-0090perturbed sampling kantorovich operatorsquantitative estimatesorder of approximationmodulus of smoothnesslipschitz classes41a3041a25 |
| spellingShingle | Costarelli Danilo De Angelis Eleonora Vinti Gianluca Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces Demonstratio Mathematica perturbed sampling kantorovich operators quantitative estimates order of approximation modulus of smoothness lipschitz classes 41a30 41a25 |
| title | Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces |
| title_full | Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces |
| title_fullStr | Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces |
| title_full_unstemmed | Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces |
| title_short | Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces |
| title_sort | quantitative estimates for perturbed sampling kantorovich operators in orlicz spaces |
| topic | perturbed sampling kantorovich operators quantitative estimates order of approximation modulus of smoothness lipschitz classes 41a30 41a25 |
| url | https://doi.org/10.1515/dema-2024-0090 |
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