Exploring q-Stancu Operators via a New Representation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908978305302528 |
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| author | Baraner, Feride Gurel, Ovgu |
| author_facet | Baraner, Feride Gurel, Ovgu |
| contents | This paper investigates the q-Stancu operators, which generalize the q-Bernstein operators, by developing a new representation in terms of the q-Pochhammer symbol. Based on this representation, some known properties are re-discovered, and a general recurrence relation for the moments is established. It is shown that higher-order moments can be expressed in terms of lower-order ones. Furthermore, the limit form of the operators is defined and their uniform convergence is proved. Finally, the moments of the limit operator and their recurrence relations are presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exploring q-Stancu Operators via a New Representation Baraner, Feride Gurel, Ovgu Functional Analysis 41A10, 41A36, 47B38 This paper investigates the q-Stancu operators, which generalize the q-Bernstein operators, by developing a new representation in terms of the q-Pochhammer symbol. Based on this representation, some known properties are re-discovered, and a general recurrence relation for the moments is established. It is shown that higher-order moments can be expressed in terms of lower-order ones. Furthermore, the limit form of the operators is defined and their uniform convergence is proved. Finally, the moments of the limit operator and their recurrence relations are presented. |
| title | Exploring q-Stancu Operators via a New Representation |
| topic | Functional Analysis 41A10, 41A36, 47B38 |
| url | https://arxiv.org/abs/2604.17498 |