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arXiv · 2604.17498

Exploring q-Stancu Operators via a New Representation

Feride Baraner·Ovgu Gurel
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Abstract

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.

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Feride Baraner, Ovgu Gurel. 2026-04-19. Exploring q-Stancu Operators via a New Representation. https://arxiv.org/abs/2604.17498

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