Exploring q-Stancu Operators via a New Representation
Functional Analysis
2026-04-21 v1
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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Cite
@article{arxiv.2604.17498,
title = {Exploring q-Stancu Operators via a New Representation},
author = {Feride Baraner and Ovgu Gurel},
journal= {arXiv preprint arXiv:2604.17498},
year = {2026}
}
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