Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus
Abstract The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval [12,∞) $[ \frac{1}{2},\infty )$. This type of modification allows a better estimation of the error on [12,∞) $[ \frac{1}{2},\infty ) $ rather than [0,∞)...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-09-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2182-8 |
| _version_ | 1819055659537137664 |
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| author | Abdullah Alotaibi |
| author_facet | Abdullah Alotaibi |
| author_sort | Abdullah Alotaibi |
| collection | DOAJ |
| description | Abstract The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval [12,∞) $[ \frac{1}{2},\infty )$. This type of modification allows a better estimation of the error on [12,∞) $[ \frac{1}{2},\infty ) $ rather than [0,∞) $[ 0,\infty )$. We establish Korovkin type result in weighted spaces and also study approximation properties with the help of modulus of continuity of order one, Lipschitz type maximal functions, and Peetre’s K-functional. Furthermore, we estimate the degrees of approximations of the operators by modulus of continuity of order two. |
| first_indexed | 2024-12-21T13:11:02Z |
| format | Article |
| id | doaj.art-60a0d21a74684a5891ed274bffb4b7ad |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-21T13:11:02Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-60a0d21a74684a5891ed274bffb4b7ad2022-12-21T19:02:52ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-09-012019111010.1186/s13660-019-2182-8Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculusAbdullah Alotaibi0Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz UniversityAbstract The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval [12,∞) $[ \frac{1}{2},\infty )$. This type of modification allows a better estimation of the error on [12,∞) $[ \frac{1}{2},\infty ) $ rather than [0,∞) $[ 0,\infty )$. We establish Korovkin type result in weighted spaces and also study approximation properties with the help of modulus of continuity of order one, Lipschitz type maximal functions, and Peetre’s K-functional. Furthermore, we estimate the degrees of approximations of the operators by modulus of continuity of order two.http://link.springer.com/article/10.1186/s13660-019-2182-8( p , q ) $(p,q)$ -integersDunkl analogueDunkl generalization of exponential functionSzász operatorLipschitz type maximal functionsPeetre’s K-functional |
| spellingShingle | Abdullah Alotaibi Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus Journal of Inequalities and Applications ( p , q ) $(p,q)$ -integers Dunkl analogue Dunkl generalization of exponential function Szász operator Lipschitz type maximal functions Peetre’s K-functional |
| title | Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus |
| title_full | Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus |
| title_fullStr | Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus |
| title_full_unstemmed | Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus |
| title_short | Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus |
| title_sort | approximation by a generalized class of dunkl type szasz operators based on post quantum calculus |
| topic | ( p , q ) $(p,q)$ -integers Dunkl analogue Dunkl generalization of exponential function Szász operator Lipschitz type maximal functions Peetre’s K-functional |
| url | http://link.springer.com/article/10.1186/s13660-019-2182-8 |
| work_keys_str_mv | AT abdullahalotaibi approximationbyageneralizedclassofdunkltypeszaszoperatorsbasedonpostquantumcalculus |